Question

a quadrilateral ABCD is drawn to circumference of circle prove that AB + CD= AD+BC​

Answer 1

Answer:

Step-by-step explanation:

let ABCD be the quad. which circumscribes a circle with centre O.

the quad. touches the circle at P,Q,R,S

we need to prove AB+CD=AD+BC

we know lengths of tangents drawn from an external point are equal

therefore

AP=AS     ................(1)

BP=BQ     ................(2)

CR=CQ   ...............(3)

DR=Ds   ........(4)

add (1),(2),(3),(4)

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

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

=>AB+CD=AD+BC