Question

a circle touches all the four sides of a quadrilateral ABCD prove that a b + c d is equals to BC + DA

Answer 1

Tangent drawn from external pt to circle are equal
AP = AQ. 1
DP = DS. 2
BR = BQ. 3
RC = CS. 4

Add 1,2,3and4
AP + DP + BR + RC = AQ + DS + BQ + CS.
AD + BC = AB + CD.
hence proved.

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