`A B` and `C D` are two parallel chords of a circle whose diameter is `A C` . Prove that `A B=C Ddot`

Explanation

Given: `AB` and `CD` are two chords of the circle such that `ABCD` and `AC` is the diameter of the circle.
In the triangles `CBA` and `ADC`,
`angle CBA = angle ADC = 90` [angles in the semi circle]
`angle BAC = angle ACD` [alternate interior angles]
`AC` is common.
Therefore by AAS congruency, triangles are congruent.
Thus `AB = CD (CPCT)`