Question

A circle touches all the four sides of a quadrilateral abcd

Answer 1

Dear Student;

I think Your question is not complete

But i am guessing Your question and

will give Answer according to that.

Let the circle touches side AB at point P,

BC at point Q, CD at point R, DA at point S.

we know that two tangents which are equal in length from an external point of a circle

Thus A is external point ,AP and AS are tangents to the circle

AP=AS.........(1)

similarly B,C,D are external points

BP=BQ.......(2)

CR=CQ.......(3)

DR=DS........(4)

ADDING EQUATION 1,2,3,4

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

AB. + CD. = AD. + BC

HENCE PROVED!!!!!!!

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