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A B\ a n d\ C D are two parallel chor...

`A B\ a n d\ C D` are two parallel chords of a circle whose diameter is `A C` . Prove that `A B=C D`

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To prove that the lengths of the parallel chords \( AB \) and \( CD \) are equal in a circle where \( AC \) is the diameter, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Circle and Chords**: Let \( O \) be the center of the circle. The diameter \( AC \) passes through \( O \), and the chords \( AB \) and \( CD \) are parallel to each other. 2. **Draw Perpendiculars**: Draw perpendiculars from the center \( O \) to the chords \( AB \) and \( CD \). Let these perpendiculars meet \( AB \) at point \( M \) and \( CD \) at point \( N \). ...
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