Question

A circle touches all

four sides of a quadrilateral_ABCD
prove that AB + CD=
AD+ BC​

Answer 1

Hope it helps............

Answer 2

Answer:

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Step-by-step explanation:

Let the circle touches the side AB at point P , BC at point Q , CD at R and DA at

S.

we know that :-

There could be drawn two tangents which are equal in length from an

external point of a circle.

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

AP = AS………………….(1)

Similarly B , C. and D are external points,

BP= BQ…………………..(2)

CR= CQ…………………….(3)

DR= DS……………………..(4)

Adding eqn. (1), (2) , (3) and (4)

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

or. (AP+BP)+(CR+DR) = (BQ+CQ)+(DS+AS)

or. AB+CD = BC + DA. Proved.