Question

A quadrilateral ABCD is drawn to circumscribe a circle . prove that AB+CD+=AD+ BC .​

Answer 1

Answer:

Let circle touch the side AB, BC,CD,and DA at P,Q,R and S respectively

AP=AS. (1)(TANGENTS FROM A)

BP=BQ. (2) (TANGENTS FROM B)

CA=CR. (3)

DR=DS. (4)

adding all

AB +CD = BC+DA

Answer 2

Step-by-step explanation:

Given. c( o,r)

a quadrilateral is circumscribe a circle

quadrilateral is ABCD, the circle insribe the quadrilateral at points PQRS.

to prove . AB+ CD=AD+BC

proof . since tangents drawn from the external point are equal then, AP=AS.......1

BP=BQ........2

CR=CQ........3

DR=DS.......4

Adding1,2,3,4

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

AB+CD=AD+BC