564 + Mcqs in Plane Geometry in Aptitude Page 1 McqOptions

1.	In the adjoining figure, AB \|\| CD, t is the traversal, EG and FG are the bisectors of BEE and DFE respectively, then EGF is equal to :
A.	90
B.	75
C.	80
D.	110
E.	None of these
Answer» B. 75

Discussion

2.	In the given figure, DE \|\| BC and DE : BC = 3 : 5 the ratio of the areas of ADE and the trapezium BCED.
A.	None of these
Answer» E.

Discussion

3.	If H is the orthocentre of ABC, then the orthocentre of HBC is (fig. given) :
A.	N
B.	M
C.	A
D.	L
E.	None of these
Answer» C. A

Discussion

4.	In a triangle ABC, the length of the sides AB, AC and BC are 3, 5 and 6 cm respectively. If a point D on BC is drawn such that the line AD bisects the angle A internally, then what is the length of BD?
A.	2 cm
B.	2.25 cm
C.	2.5 cm
D.	3 cm
E.	None of these
Answer» C. 2.5 cm

Discussion

5.	X, Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD. AY and DX are joined intersecting in P; CX and BY are joined intersecting in Q. Then PXQY is a :
A.	Rectangle
B.	Rhombus
C.	Parallelogram
D.	Square
E.	None of these
Answer» D. Square

Discussion

6.	ABCD is a rhombus with ABC = 56 , then ACD is equal to :
A.	90
B.	60
C.	56
D.	62
E.	None of these
Answer» E. None of these

Discussion

7.	In the given figure, In a ABC , B = C. If AM is the bisector of BAC and AN BC, then MAN is equal to :
A.	B + C
B.	None of these
Answer» E.

Discussion

8.	ABCD is a square, F is mid point of AB and E is a point on BC such that BE is one-third of BC. If area of FBE = 108 m², then the length of AC is:
A.	63 m
B.	36 2 m
C.	63 2 m
D.	72 2 m
E.	None of these
Answer» C. 63 2 m

Discussion

9.	The diagonals of a rectangle ABCD meet at 0. If BOC = 44 , then OAD is equal to :
A.	90
B.	60
C.	100
D.	68
E.	None of these
Answer» E. None of these

Discussion

10.	ABCD is a parallelogram P, Q, R and S are points on sides AB, BC, CD and DA respectively such that AP = DR. If the area of the parallelogram ABCD is 16 cm², then the area of the quadrilateral PQRS is:
A.	6 cm
B.	6.4 cm
C.	4 cm
D.	8 cm
E.	None of these
Answer» E. None of these

Discussion

11.	ABC is a in which AB = AC and D is a point on AC such that BC² = AC CD. Then :
A.	BD = DC
B.	BD = BC
C.	BD = AB
D.	BD = AD
E.	None of these
Answer» C. BD = AB

Discussion

12.	In the accompanying figure, AB is one of the diameters of the circle and OC is perpendicular to it through the centre O. If AC is 7 2 cm, then what is the area of the circle in cm²?
A.	24.5
B.	49
C.	98
D.	154
E.	None of these
Answer» E. None of these

Discussion

13.	If two diameters of a circle intersect each other at right angles, then the quadrilateral formed by joining here end points is a :
A.	Rhombus
B.	Rectangle
C.	Square
D.	Parallelogram
E.	None of these
Answer» D. Parallelogram

Discussion

14.

ABC is a right angled triangle in which C = 90 . If BC = a, AB = c, CA = b and the length of perpendicular from C to AB be p, then,
1 + 1 = ?
a b

A.

B.

None of these

Answer» D.

Discussion

15.	In the given figure, the side BC of a ABC is produced on both sides. Then 1 + 2 is equal to :
A.	A + 180
B.	180 A
C.	A + 90
D.	None of these
Answer» B. 180 A

Discussion

16.	A chord of length 10 cm subtends an angle 120 at the centre of a circle . Distance of the chord from the centre is
A.	5
B.	cm.
C.	5 cm.
Answer» D.

Discussion

17.	In the given figure, side BC of ABC is produced to form ray BD and CE \|\| BA. Then ACD is equal to :
A.	A - B
B.	A + B
C.	None of these
Answer» D.

Discussion

18.	Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?
A.	BC
Answer» C.

Discussion

19.	The area of two similar s are 121 cm² and 81 cm² respectively. What is the ratio of their corresponding heights (altitudes):
A.	None of these
Answer» B.

Discussion

20.	If the sides of a triangle are produced then the sum of the exterior angles i.e., a + b + c is equal to :
A.	180
B.	90
C.	360
D.	270
E.	None of these
Answer» D. 270

Discussion

21.	In ABC, the median BE intersects AC at E, if BG = 6 cm, where G is the centro-id, then BE is equal to :
A.	7 cm
B.	9 cm
C.	8 cm
D.	10 cm
E.	None of these
Answer» C. 8 cm

Discussion

22.	In fig, AB = AC, D is a point on AC and E on AB such that AD = ED = EC = BC. Then A : B :
A.	1 : 2
B.	2 : 1
C.	3 : 1
D.	1 : 3
E.	None of these
Answer» E. None of these

Discussion

23.	In a ABC, AD intersects A and BC. If BC = a, AC = b and AB = c, Then :
A.	None of these
Answer» C.

Discussion

24.

In the given figure DE||BC and AD : DB = 5 : 4,
Then ar( DFE)
ar( CFB)

A.

None of these

Answer» B.

Discussion

25.	In a ABC, the bisectors of B and C intersect each other at a point O. Then BOC is equal to :
A.	None of these
Answer» D.

Discussion

26.

In the fig. XY || AC and XY divides triangular region ABC into two part equal in area.
Then AX is equal to :
AB

A.

None of these

Answer» E.

Discussion

27.	Two poles of ht. a and b meters are p meters apart (b > a). The height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is :
A.	None of these
Answer» D.

Discussion

28.	In the given figure, what is the length of AD in terms of b and c :
A.	None of these
Answer» E.

Discussion

29.	If the internal bisectors of angles ABC and ACB of ABC intersect at point O, then BOC = ?
A.
B.
C.	90 A
Answer» C. 90 A

Discussion

30.	If P and Q are the mid points of the sides CA and GB respectively of a triangle ABC, right-angled at C. Then the value of 4 (AQ² + BP²) is equal to :
A.	4 BC
B.	5 AB
C.	2 AC
D.	2 BC
E.	None of these
Answer» C. 2 AC

Discussion

31.	G is the centroid of the equilateral triangle ABC. If AB = 10 cm then length of AG is
A.	10
B.	cm
C.	10
D.	cm
Answer» C. 10

Discussion

32.	In a quadrilateral ABCD, B = 90 and AD² = AB² + BC² + CD², then ACD is equal to:
A.	90
B.	60
C.	30
D.	20
E.	None of these
Answer» B. 60

Discussion

33.	PQRS is a square. The SRP is equal to :
A.	45
B.	90
C.	100
D.	60
E.	None of these
Answer» B. 90

Discussion

34.	The two sides of a right triangle containing the right angle measure 3 cm and 4 cm. The radius of the in circle of the triangle is :
A.	3.5 cm
B.	1.75 cm
C.	1 cm
D.	0.875 cm
E.	None of these
Answer» D. 0.875 cm

Discussion

35.	We have an angle of 2¹/₂ .How big it will look through a glass that magnifies things three times?
A.	None of these
Answer» E.

Discussion

36.	If AD, BE and CF are medians of ABC, then which one of the following statements is correct ?
A.	(AD + BE + CF) < AB + BC + CA
B.	AD+BE + CF > AB + BC + CA
C.	AD+BE + CF = AB + BC + CA
D.	AD+BE+CF=
E.	(AB+BC+ CA)
Answer» B. AD+BE + CF > AB + BC + CA

Discussion

37.	Two circles C₁ and C₂ touch each other internally at P. Two lines PCA and PDB meet the circles C₁ in C, D and C₂ in A, B respectively. If BDC = 120 , then the value of ABP is equal to
A.	60
B.	80
C.	100
D.	120
Answer» B. 80

Discussion

38.	In ABC, AB = a b, AC = a + b and BC = 2ab, then find angle B.
A.	60
B.	30
C.	90
D.	45
Answer» D. 45

Discussion

39.	The altitude of an equilateral triangle of side 2/ 3 cm is :
A.	4/3 m
B.	4/
C.	m
D.	4/3 m
E.	1 m
Answer» E. 1 m

Discussion

40.	In any triangle ABC the internal bisector of ABC and the external bisector of other base angle meet at point E. Then BEC = ?
A.	A
B.	2 A
Answer» D.

Discussion

41.	In a circular lawn, there is a 16 m long path in the form of a chord. If the path is 6 m away from the center of the lawn, then find the radius of the circular lawn.
A.	16 m
B.	6 m
C.	10 m
D.	8 m
E.	None of these
Answer» D. 8 m

Discussion

42.	ABCD is a parallelogram and X, Y are the mid-points of sides AB and CD respectively. Then quadrilateral AXCY is a :
A.	parallelogram
B.	rhombus
C.	square
D.	rectangle
E.	None of these
Answer» B. rhombus

Discussion

43.	In the figure, BD and CD are angle bisectors of ABC and ACE, respectively. Then BDC is equal to :
A.	BAC
B.	2 BAC
C.	None of these
Answer» D.

Discussion

44.	In a ABC, the sides AB and AC are produced to P and Q respectively. The bisectors of OBC and QCB intersect at a point O. Then BOC is equal to:
A.	None of these
Answer» C.

Discussion

45.	Two chords AB and CD of a circle with centre O intersect at point P within the circle. AOC + BOD = ?
A.	APC
B.
C.	2 APC
D.
E.	None of these
Answer» C. 2 APC

Discussion

46.	ABCD is a trapezium whose side AD is parallel to BC. Diagonals AC and BD intersect at O. If AO = 3 , CO = x - 3 , BO = 3x - 19 and DO = x - 5 , the value(s) of x will be :
A.	7, 6
B.	12, 6
C.	7, 10
D.	8, 9
Answer» E.

Discussion

47.	AB and CD are two parallel chords on the opposite sides of the centre of the circle. If AB = 10 cm, CD = 24 cm and the radius of the circle is 13 cm, the distance between the chords is
A.	17 cm
B.	15 cm
C.	16 cm
D.	18 cm
Answer» B. 15 cm

Discussion

48.	The angle subtended by a chord at its centre is 60 , then the ratio between chord and radius is
A.	1 : 2
B.	1 : 1
C.
D.	: 1
E.	2 : 1
Answer» C.

Discussion

49.	A, B, C are three points on the circumference of a circle and if AB = AC = 5 2 cm and BAC = 90 , find the radius.
A.	10 cm
B.	5 cm
C.	20 cm
D.	15 cm
Answer» C. 20 cm

Discussion

50.	A triangle ABC is inscribed in a circle and the bisectors of the angles A, B and C meet the circumference at P, Q and R respectively. The angles of the triangle PQR respectively are
A.
B.
C.	None of these
Answer» D.

Discussion

Explore topic-wise MCQs in Aptitude.

In the adjoining figure, AB || CD, t is the traversal, EG and FG are the bisectors of BEE and DFE respectively, then EGF is equal to :

In the given figure, DE || BC and DE : BC = 3 : 5 the ratio of the areas of ADE and the trapezium BCED.

If H is the orthocentre of ABC, then the orthocentre of HBC is (fig. given) :

In a triangle ABC, the length of the sides AB, AC and BC are 3, 5 and 6 cm respectively. If a point D on BC is drawn such that the line AD bisects the angle A internally, then what is the length of BD?

X, Y are the mid-points of opposite sides AB and DC of a parallelogram ABCD. AY and DX are joined intersecting in P; CX and BY are joined intersecting in Q. Then PXQY is a :

ABCD is a rhombus with ABC = 56 , then ACD is equal to :

In the given figure, In a ABC , B = C. If AM is the bisector of BAC and AN BC, then MAN is equal to :

ABCD is a square, F is mid point of AB and E is a point on BC such that BE is one-third of BC. If area of FBE = 108 m2, then the length of AC is:

The diagonals of a rectangle ABCD meet at 0. If BOC = 44 , then OAD is equal to :

ABCD is a parallelogram P, Q, R and S are points on sides AB, BC, CD and DA respectively such that AP = DR. If the area of the parallelogram ABCD is 16 cm2, then the area of the quadrilateral PQRS is:

ABC is a in which AB = AC and D is a point on AC such that BC2 = AC CD. Then :

In the accompanying figure, AB is one of the diameters of the circle and OC is perpendicular to it through the centre O. If AC is 7 2 cm, then what is the area of the circle in cm2?

If two diameters of a circle intersect each other at right angles, then the quadrilateral formed by joining here end points is a :

ABC is a right angled triangle in which C = 90 . If BC = a, AB = c, CA = b and the length of perpendicular from C to AB be p, then, 1 + 1 = ?a b

In the given figure, the side BC of a ABC is produced on both sides. Then 1 + 2 is equal to :

A chord of length 10 cm subtends an angle 120 at the centre of a circle . Distance of the chord from the centre is

In the given figure, side BC of ABC is produced to form ray BD and CE || BA. Then ACD is equal to :

Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ?

The area of two similar s are 121 cm2 and 81 cm2 respectively. What is the ratio of their corresponding heights (altitudes):

If the sides of a triangle are produced then the sum of the exterior angles i.e., a + b + c is equal to :

In ABC, the median BE intersects AC at E, if BG = 6 cm, where G is the centro-id, then BE is equal to :

In fig, AB = AC, D is a point on AC and E on AB such that AD = ED = EC = BC. Then A : B :

In a ABC, AD intersects A and BC. If BC = a, AC = b and AB = c, Then :

In the given figure DE||BC and AD : DB = 5 : 4, Then ar( DFE)ar( CFB)

In a ABC, the bisectors of B and C intersect each other at a point O. Then BOC is equal to :

In the fig. XY || AC and XY divides triangular region ABC into two part equal in area.Then AXis equal to :AB

Two poles of ht. a and b meters are p meters apart (b > a). The height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is :

In the given figure, what is the length of AD in terms of b and c :

If the internal bisectors of angles ABC and ACB of ABC intersect at point O, then BOC = ?

If P and Q are the mid points of the sides CA and GB respectively of a triangle ABC, right-angled at C. Then the value of 4 (AQ2 + BP2) is equal to :

G is the centroid of the equilateral triangle ABC. If AB = 10 cm then length of AG is

In a quadrilateral ABCD, B = 90 and AD2 = AB2 + BC2 + CD2, then ACD is equal to:

PQRS is a square. The SRP is equal to :

The two sides of a right triangle containing the right angle measure 3 cm and 4 cm. The radius of the in circle of the triangle is :

We have an angle of 21 /2 .How big it will look through a glass that magnifies things three times?

If AD, BE and CF are medians of ABC, then which one of the following statements is correct ?

Two circles C1 and C2 touch each other internally at P. Two lines PCA and PDB meet the circles C1 in C, D and C2 in A, B respectively. If BDC = 120 , then the value of ABP is equal to

In ABC, AB = a b, AC = a + b and BC = 2ab, then find angle B.

The altitude of an equilateral triangle of side 2/ 3 cm is :

In any triangle ABC the internal bisector of ABC and the external bisector of other base angle meet at point E. Then BEC = ?

In a circular lawn, there is a 16 m long path in the form of a chord. If the path is 6 m away from the center of the lawn, then find the radius of the circular lawn.

ABCD is a parallelogram and X, Y are the mid-points of sides AB and CD respectively. Then quadrilateral AXCY is a :

In the figure, BD and CD are angle bisectors of ABC and ACE, respectively. Then BDC is equal to :

In a ABC, the sides AB and AC are produced to P and Q respectively. The bisectors of OBC and QCB intersect at a point O. Then BOC is equal to:

Two chords AB and CD of a circle with centre O intersect at point P within the circle. AOC + BOD = ?

ABCD is a trapezium whose side AD is parallel to BC. Diagonals AC and BD intersect at O. If AO = 3 , CO = x - 3 , BO = 3x - 19 and DO = x - 5 , the value(s) of x will be :

AB and CD are two parallel chords on the opposite sides of the centre of the circle. If AB = 10 cm, CD = 24 cm and the radius of the circle is 13 cm, the distance between the chords is

The angle subtended by a chord at its centre is 60 , then the ratio between chord and radius is

A, B, C are three points on the circumference of a circle and if AB = AC = 5 2 cm and BAC = 90 , find the radius.

A triangle ABC is inscribed in a circle and the bisectors of the angles A, B and C meet the circumference at P, Q and R respectively. The angles of the triangle PQR respectively are

ABCD is a square, F is mid point of AB and E is a point on BC such that BE is one-third of BC. If area of FBE = 108 m², then the length of AC is:

ABCD is a parallelogram P, Q, R and S are points on sides AB, BC, CD and DA respectively such that AP = DR. If the area of the parallelogram ABCD is 16 cm², then the area of the quadrilateral PQRS is:

ABC is a in which AB = AC and D is a point on AC such that BC² = AC CD. Then :

In the accompanying figure, AB is one of the diameters of the circle and OC is perpendicular to it through the centre O. If AC is 7 2 cm, then what is the area of the circle in cm²?

ABC is a right angled triangle in which C = 90 . If BC = a, AB = c, CA = b and the length of perpendicular from C to AB be p, then,
1 + 1 = ?
a b

The area of two similar s are 121 cm² and 81 cm² respectively. What is the ratio of their corresponding heights (altitudes):

In the given figure DE||BC and AD : DB = 5 : 4,
Then ar( DFE)
ar( CFB)

In the fig. XY || AC and XY divides triangular region ABC into two part equal in area.
Then AX is equal to :
AB

If P and Q are the mid points of the sides CA and GB respectively of a triangle ABC, right-angled at C. Then the value of 4 (AQ² + BP²) is equal to :

In a quadrilateral ABCD, B = 90 and AD² = AB² + BC² + CD², then ACD is equal to:

We have an angle of 2¹/₂ .How big it will look through a glass that magnifies things three times?

Two circles C₁ and C₂ touch each other internally at P. Two lines PCA and PDB meet the circles C₁ in C, D and C₂ in A, B respectively. If BDC = 120 , then the value of ABP is equal to