Prove that the semicircular angle is a right angle.

According to question, the figure can be drawn as shown, Here, A O B is a straight line passing through center O . So, angle subtended by the arc A B at O is ∠ A O B = 180 ° 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. ∴ ∠ A O B = 2 ∠ A P B ( ∠ A O B is the subtended at center which is equal to 180 ° and ∠ A P B is the angle made at any point on the circle.) ⇒ ∠ A O B 2 = ∠ A P B ⇒ ∠ A P B = 180 ° 2 ⇒ ∠ A P B = 90 ° Hence, it can be said that the angle in a semicircle is a right angle.