Mathematics
Prove that in a cyclic trapezium, the non-parallel sides are equal.
Circles
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Answer
Let ABCD be the cyclic trapezium in which AB || DC, AC and BD are the diagonals.
It's seen that chord AD subtends ∠ABD and chord BC subtends ∠BDC at the circumference of the circle.
But, ∠ABD = ∠BDC [Alternate angles are equal]
∴ Chord AD must be equal to chord BC [As equal chord subtends equal angles at circumference]
⇒ AD = BC.
Hence, proved that in a cyclic trapezium, the non-parallel sides are equal.
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