Get live Maths 1-on-1 Classs - Class 6 to 12
Angle in a semicircle is a right angle
Last updated at March 16, 2023 by Teachoo
Theorems
Theorem 10.1
Theorem 10.2 Important
Theorem 10.3 Important Deleted for CBSE Board 2023 Exams
Theorem 10.4
Theorem 10.5
Theorem 10.6 Important
Theorem 10.7
Theorem 10.8 Important
Theorem 10.9
Theorem 10.10 Important
Theorem 10.11
Theorem 10.12 Important
Angle in a semicircle is a right angle Important You are here
Chapter 10 Class 9 Circles
Serial order wise
Transcript
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.
