Question

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Prove that angle in a semi circle is 90°

Answer 1

As AOB is 180°, it follows that APB is90°. AOB is the diameter, so it follows that the angle in a semicircle is always a right angle:

Proof : Label the diameter endpoints A and B, the top point C and the middle of the circle M. Label the acute anglesat A and B Alpha and Beta

The angle at the centre (AOB) is twice the angle at the circumference (APB). As AOB is 180°, it follows that APB is 90°.

AOB is the diameter, so it follows that the angle in a semicircle is always a right angle:

Answer 2

Angle formed by diameter of the circle is 180°

And we know that in circle , the opposite angle of another angle from centre is half of it .

Therefore , angle in a semi circle is 90°