Question

A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the given figure. Show that `(AB + CD)/(AD + BC)` = 1.

Answer 1

Tangents drawn to a circle from an external point are equal.

So, AP = AS,

PB = BQ, 

CR = CQ,

DR = DS

On adding the above equations,

(AP + PB) + (CR + RD) = (AS + BQ) + (CQ + DS)

⇒ AB + CD = AD + BC

⇒ `(AB + CD)/(AD + BC)` = 1