A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.

Question

Philoid · Accepted Answer

To prove: AB + CD = AD + BC.

Proof: AS = AP ( Length of tangents from an external point to a circle are equal)

BQ = BP

CQ = CR

DS = DR

AS + BQ + CQ + DS = AP + BP + CR + DR

(AS + DS) + ( BQ + CQ) = (AP + BP) + (CR + DR)

AD + BC = AB +CD