Question

1) Prove that angle inscribed in a semicircle is a right angle.​

Answer 1

Answer:

Prove that the angle in a semicircle is a right angle.

∴∠AOB=2∠APB (∠AOB is the subtended at center which is equal to 180∘ and ∠APB is the angle made at any point on the circle.) Hence, it can be said that the angle in a semicircle is a right angle

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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∠PAQ

∠POQ/2 =∠PAQ

180 / 2 =∠PAQ

∠PAQ=90

Hence proved.

Step-by-step explanation:

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