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 its helps you.

Answer 2

in the figure
first join CB & AD then
in ABC and CDA
AC=AC(common)
angle CBA=angel ADC =90 degree
angle BCA=angle DCA (alternate angles)
ABC congruent ADC
AB=CD (CPCT)