Question

AB and CD are two parallel chords of a circle whose diameter is AC. Prove that AB=CD

Answer 1

given: AB and CD are two chords of the circle such that ABCD and AC is the diameter of the circle.

TPT: AB = CD

proof:

in the triangles CBA and ADC,

∠CBA = ∠ADC = 90 [angles in the semi circle]

∠BAC = ∠ACD [alternate interior angles]

AC is common.

therefore by AAS congruency, triangles are congruent.

thus AB = CD [CPCT]

hope this helps you.