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प्रश्न
P is the mid-point of an arc APB of a circle. Prove that the tangent drawn at P will be parallel to the chord AB.
उत्तर
Join AP and BP.
Since TPS is a tangent and PA is the chord of the circle.
∠BPT = ∠PAB ...(Angles in alternate segments)
But
∠PBA = ∠PAB ...(∵ PA = PB)
∴ ∠BPT = ∠PBA
But these are alternate angles
∴ TPS || AB
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