A circle touches all the four sides of a quadrilateral ABCD.prove that AB+CD=BC+DA
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PROOF: let the circle touch the sides AB, BC, CD, and DA of quadrilateral at points P, Q, R, S.
AP=AS , DS=DR, CR=CQ, BQ=BP. ........(1)
A-P-B, B-Q-C, C-R-D, A-S-D. ........(2)
AB+CD = AP+AB+CR+RD
= AS+BQ+CQ+DS
= AS+DS+BQ+CQ
= AD + BC
hence, AB+CD=AD+BC. ......proved
HOPE THAT THIS WILL HELP YOU..
PROOF: let the circle touch the sides AB, BC, CD, and DA of quadrilateral at points P, Q, R, S.
AP=AS , DS=DR, CR=CQ, BQ=BP. ........(1)
A-P-B, B-Q-C, C-R-D, A-S-D. ........(2)
AB+CD = AP+AB+CR+RD
= AS+BQ+CQ+DS
= AS+DS+BQ+CQ
= AD + BC
hence, AB+CD=AD+BC. ......proved
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