Mock test 1 - Q13 - pending

Q13. Let ABCD be a trapezium in which AB||CD and AD perpendicular to AB. Suppose ABCD has an incircle which touches AB at Q and CD at P. Given that PC = 36 and QB = 49, Find PQ. 
Solution:

Let incircle touch BC at R
CR = 36, BR = 49
Further let inradius = r
So AQ = PD = r and AD = 2r
Let perpendicular from C meet AB at S
So BS = 13, BC = 85
(CS)^2 = 85^2 - 13^2 = 98*72 = 84^2
CS = 84 = PQ








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