Equal Chords of a Circle Subtend Equal Angle at the Centre
Equal Chords of a Circle Subtend Equal Angle at the Centre
Theorem 1 Equal chords of a circle subtend equal angles at the centre.
Given A circle C (O,r) and its two equal chords AB and CD. TO PROVE PROOF In triangles AOB and COD, we have AB = CD [ Given ] OA = OC [ Each equal to r ] OB = OD [ Each equal to r ] So, by SSS- criterion of congruence, we have
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Theorem 2 IF the angles subtended by two chords of a circle at the centre are equal , the chords are equal.
Given Two chords AB and CD of a circle C (O,r) such that TO PROVE AB = CD PROOF In triangles AOB and COD, we have So, by SAS- criterion of congruence, we have
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Illustration: Inthe given figure AB = PQ and
Solution: in the figure it is given AB = PQ We know that equal Chords subtends equal angle at the centre
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| Right Option : A | |||||
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| Right Option : C | |||||
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In a circle with centre O, major arc PQ subtends an angle at the centre. The angle formed is | |||
| Right Option : D | |||
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