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Angle in a semicircle is a right angle - Part 2

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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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.