Vicky Singh

Angle in a semicircle is right angle

- Feb. 1, 2017, 10:48 p.m.Teachoo Expert
Hi Vicky

Please check http://teachoo.com/5521/1097/Angle-in-a-semicircle-is-a-right-angle/category/Theorems/ also.

Textual version of the answe

Theorem : Angle subtended by a diameter/semicircle on any point of circle is 90° right angle Given : A circle with centre at 0. PQ is the diameter of circle subtending ∠PAQ at point A on circle. To Prove : ∠PAQ = 90° Proof : Now, POQ is a straight line passing through center O. ∴ Angle subtended by arc PQ at O is ∠POQ = 180° Also, By theorem 10.8 : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. Thus, ∠ POQ = 2∠PAQ ∠ POQ/2 = ∠PAQ 180° = ∠PAQ 90° = ∠PAQ ∠PAQ = 90° Hence, Proved.

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