Mathematics
In the given figure, arc AC and arc BD are two equal arcs of a circle. Prove that chord AB and chord CD are parallel.
Answer
We know that,
If two arcs are equal, they subtend equal angles at centre, thus they will also subtend equal angle at the circumference.
⇒ ∠CDA = ∠BAD
These angles are alternate interior angles formed by transversal AD with lines CD and AB.
⇒ AB ∥ CD.
Hence, proved that chord AB and chord CD are parallel.
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