Question

Prove: Angle subtended by a semicircular arc (or a diameter) on the circle is always a right angle.​

Answer 1

Step-by-step explanation:

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.) ... Also, Angle subtended by any straight line when moved from one point to another point forming an arc on the line is 180°....

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Answer 2

Answer:

To prove : ∠APB=90

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∵ We know angle subtended by an arc at centre is double the angle subtended at any point or circumference.

⇒ Angle subtended by arc AB at O= Double the angle subtended at P

⇒∠AOB=2∠APB

∵AOB is a straight line.

⇒∠AOB=180

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⇒2∠APB=180

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⇒∠APB=90

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∴ Angle subtended by arc AB or semi circle is 90

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