. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.Answer:Draw the diagram as shown below.Here, AB is the tangent that is drawn on the circle from a point A.So, the radius OB will be perpendicular to AB i.e. OB ⊥ ABWe know, OA = 5cm and AB = 4 cmNow, In △ABO,OA2\xa0=AB2+BO2\xa0(Using Pythagoras theorem)52\xa0= 42+BO2BO2\xa0= 25-16BO2\xa0= 9BO = 3So, the radius of the given circle i.e. BO is 3 cm.7. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.Answer:Draw two concentric circles with the center O. Now, draw a chord AB in the larger circle which touches the smaller circle at a point P as shown in the figure below.From the above diagram, AB is tangent to the smaller circle to point P.∴ OP ⊥ ABUsing Pythagoras theorem in triangle OPA,OA2= AP2+OP252\xa0= AP2+32AP2\xa0= 25-9AP = 4Now, as OP ⊥ AB,Since the perpendicular from the center of the circle bisects the chord, AP will be equal to PBSo, AB = 2AP = 2×4 = 8 cmSo, the length of the chord of the larger circle is 8 cm
???
I should study