In Figure 3, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of the side AD.
Let the inscribed circle touch sides AB, BC, CD and DA of quadrilateral ABCD at P, Q, R and S respectively.
It is known that the lengths of tangents drawn from an external point to a circle are equal.
∴ AS = AP, DS = DR, BP = BQ, CR = CQ
= AS + DS
= AP + DR
= (6 − PB) + (8 − CR)
= 14 cm − BQ − CQ [(Using (1)]
= 14 cm − (BQ + CQ)
= 14 cm − BC
= (14 − 9) cm
= 5 cm
Thus, the length of side AD is 5 cm
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