Last updated at Aug. 24, 2021 by

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.

Theorems

Theorem 10.1

Theorem 10.2 Important

Theorem 10.3 Important

Theorem 10.4

Theorem 10.5 Deleted for CBSE Board 2022 Exams

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 (Term 2)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.