Question

A quadrilateral is drawn to circumscribe a circle prove that the sum of opposite sides are equal

Answer 1

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Answer 2

Sum of opposite sides are equal if A quadrilateral is drawn to circumscribe a circle

Step-by-step explanation:

Let say ABCD is a Quadrilateral Circumscribing a Circle

AB touching at P

BC touching at Q

CD touching at R

AD touching at S

AP = AS  ( Equal tangent)

BP = BQ

CQ = CR

DR = DS

AB + CD  = AP + BP  + CR + DR

= AS + BQ + CQ + DS

= AS + DS + BQ + CQ

= AD + BC

AB + CD = AD + BC

sum of opposite sides are equal

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