Question

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

Answer 1

Solution: AP = AS (tangents from a point are always
equal) Similarly, PB = BQ CQ = CR DR = DS
AB = AP + PB  BC = BQ + CQ = PB + CQ
CD = CR + DR = CQ + DR  AD = DS + AS = DR + AP
AB + CD = AP + PB + CQ + DR ………….. (i)
AD + BC = DR + AP + PB + CQ …………… (ii)
From equation (i) and (ii) it is clear AB + CD = AD + BC