In the following figure, a circle is inscribed in the quadrilateral ABCD.
If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.
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In the following figure, a circle is inscribed in the quadrilateral ABCD.
If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.
In the following figure, a circle is inscribed in the quadrilateral ABCD.
If BC = 38 cm, QB = 27 cm, DC = 25 cm and that AD is perpendicular to DC, find the radius of the circle.
From the figure we see that BQ = BR = 27 cm (since length of the tangent segments from an external point are equal)
As BC = 38 cm
CR = CB − BR = 38 − 27
= 11 cm
Again,
CR = CS = 11cm (length of tangent segments from an external point are equal)
Now, as DC = 25 cm
∴ DS = DC − SC
= 25 − 11
= 14 cm
Now, in quadrilateral DSOP,
∠PDS = 90° (given)
∠OSD = 90°, ∠OPD = 90° (since tangent is perpendicular to the radius through the point of contact)
DSOP is a parallelogram
OP ∥ SD and PD ∥ OS
Now, as OP = OS (radii of the same circle)
OPDS is a square. ∴ DS = OP = 14cm
∴ radius of the circle = 14 cm