Mathematics
In the given figure, a circle is inscribed in quadrilateral ABCD. If BC = 38 cm, BQ = 27 cm, DC = 25 cm and AD ⟂ 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.
Related Questions
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In the given figure, quadrilateral ABCD is circumscribed and AD ⟂ AB. If the radius of the incircle is 10 cm, find the value of x.
In the given figure, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°, find the values of x, y and z.
In the given figure, TP and TQ are two tangents to the circle with centre O, touching at A and C respectively. If ∠BCQ = 55° and ∠BAP = 60°, find :
(i) ∠OBA and ∠OBC
(ii) ∠AOC
(iii) ∠ATC
