Question

किसी वृत्त के एक वृत्तचाप द्वारा निर्मित सम्मुख केन्द्र पर बना कोण उसकी शेष परिधि पर बने कोण का doguna hota है। ​

Answer 1

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Class 9

>>Maths

>>Circles

>>Angles in the Same Segment

>>Prove that the angle subten...

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Prove that 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 .

Medium

Solution

verified

Given :

An arc PQ of a circle subtending angles POQ at the centre O and PAQ at a point A on the remaining part of the circle.

To prove : ∠POQ=2∠PAQ

To prove this theorem we consider the arc AB in three different situations, minor arc AB, major arc AB and semi-circle AB.

Construction :

Join the line AO extended to B.