Mathematics
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.
Answer
From figure,
⇒ BR = BQ = 27 cm [∵ Length of tangents form an external point to a circle are equal.]
⇒ CR = BC - BR = 38 - 27 = 11 cm.
⇒ CR = CS = 11 cm [∵ Length of tangents form an external point to a circle are equal.]
⇒ DS = DC - CS = 25 - 11 = 14 cm.
In quadrilateral DSOP,
⇒ ∠SDP + ∠DPO + ∠OSD + ∠POS = 360°
⇒ 90° + 90° + 90° + ∠POS = 360°
⇒ ∠POS = 360° - 270° = 90°.
Since, all angles are 90° and OS = OP [∵ Both equal to radius of same circle]
Hence, proved that DPOS is a square.
OP = DS = 14 cm.
Hence, radius of circle = 14 cm.
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