Question

Prove that angle in semicircle is right angle.​

Answer 1

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Now POQ is a straight line passing through center O.

∴ Angle subtended by arc PQ at O is

∠POQ=180°

The angle subtended by an arc at the center is double the angle subtended by it any point on the remaining part of the circle.

$∴∠POQ=2∠PAQ$

$\frac{∠POQ}{2} = ∠PAQ$

$\frac{180}{2} = ∠PAQ$

$∠PAQ=90$

Hence Proved

Answer 2

Answer:

Now POQ is a straight line passing through center O.

∴ Angle subtended by arc PQ at O is

∠POQ=180°

The angle subtended by an arc at the center is double the angle subtended by it any point on the remaining part of the circle.

∴∠POQ=2∠POQ

<POQ / 2 = ∠POQ

180/2 = <POQ.

∠PAQ=90