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Question
In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD then the length of Q CD is ______.
Options
11 cm
15 cm
20 cm
21 cm
MCQ
Fill in the Blanks
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Solution
In the given figure, a circle is inscribed in a quadrilateral ABCD touching its sides AB, BC, CD and AD at P, Q, R and S respectively. If the radius of the circle is 10 cm, BC = 38 cm, PB = 27 cm and AD ⊥ CD then the length of Q CD is 21 cm.
Explanation:
BQ = PB = 27 cm
CQ = BC – BQ
= (38 – 27) cm
= 11 cm
CR = CQ = 11 cm
Join OR. Then, SDRO is a square.
∴ DR = SO = radius = 10 cm.
And so, CD = DR + CR
= (10 + 11) cm
= 21 cm
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