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Let A B C D be a trapezium in which A B | C D and A D A B . Suppose A B C D has an incircle which touches AB at Q and CD at P . Given that PC =36 and QB =49 , Find PQ.

Correct answer

84

Step-by-step solution

Let incircle touch B C at R So, CR =36, BR =49 Further let inradius =r So, AQ = PD = r & AD =2 r Let perpendicular from C meet AD at S So, B S=13, B C=85 Now, ( CS )^2=85^2-13^2=98 72=49 144 So CS =7 12=84 Hence PQ =84

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