A circle touches sides of a $□$ ABCD. AB=5.BC=8. CD=6. Find AD.

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Solution

$\begin{matrix} A c i r c l e t o u c h e s t h e s i d e s A B, B C, C D a n d C D a n d D A o f q u a d r i l a t e r a l A B C D a t P, Q, R & S l e n g t h o f t a n g e n t s d r a w n f r o m a n e x t e r n a l p o i n t o f c i r c l e a r e e q u a l A P = A S, B P = B Q, C Q = C K \Rightarrow A D = A B + C D - B C = 5 + 6 - 8 = 11 - 8 3 c m l e n g t h o f A D = 3 c m \end{matrix}$

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