Question

(11) Prove : Suppose two chords of a circle intersect each other in the interior of the
circle then the product of the lengths of the two segments of one chord is equal
to the product of the lengths of the two segments of the other chord.​

Answer 1

AB and CD are two chords in a circle, they intersect inside the circle, Each chord is cut into two segments at the point of where they intersect. One chord is cut into two line segments AO and OB. The other into the segments CO and OD.

This theorem states that A×B is always equal to C×D no matter where the chords are.