Listen NCERT Audio Books to boost your productivity and retention power by 2X.
A quadrilateral is drawn to circumscribe a circle. Prove that the sums of opposite sides are equal.
Let us consider a quadrilateral ABCD, And a circle is circumscribed by ABCD
Also, Sides AB, BC, CD and DA touch circle at P, Q, R and S respectively.
To Proof : Sum of opposite sides are equal, i.e. AB + CD = AD + BC
In the Figure,
As tangents drawn from an external point are equal.
AP = AS
[tangents from point A]
BP = BQ
[tangents from point B]
CR = CQ
[tangents from point C]
DR = DS
[tangents from point D]
Add the above equations
AP + BP + CR + DR = AS + BQ + CQ + DS
AB + CD = AS + DS + BQ + CQ
AB + CD = AD + BC