Question

if circle touches allthe sides of quadrilateral ABCD,then prove that AB+CD=BC+AD​

Answer 1

Step-by-step explanation:

Let the circle touches the sides AB,BC,CD,DA of □ABCD at point P,Q,R,S respectively.

AP=AS,DS. =DR, CR=CQ ,BQ=BP and A-P-B, B -Q -C, C- R- D, A- S- D

now, AB+CD=AP+PB+CR+RD

=AS+ BQ +CQ+ DS

=AS+ DS +BQ +CQ

=AD +BC

thus, AB+CD=AD+BC