Question

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



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Answer 1

Answer:

Angle subtended in a semicircle is a right angle

Step-by-step explanation:

Here, AOB is a straight line passing through center O.

∴ Angle subtended by the arc AB at O is

∠AOB=180∘

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

∴∠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.)

∠AOB2=∠APB

180∘2=∠APB

∠APB=90∘

Hence, it can be said that the angle in a semicircle is a right angle.

Answer 2

Answer:

Step-by-step explanation:

See the pic

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