Maths / Circles / Equal Chords of a Circle Subtend Equal Angle at the Centre

QUESTION
 

Prove that equal chords of a circle subtend equal angles at the centre of the circle.

EXPLANATION
Explain TypeExplanation Content
Text

Given : AB = CD

To prove: large angle1 = large angle2

proof : In large DeltaAOB and large Delta COD,

 AO = OC    (Radii of the circle)

 AB = CD  (Given)

BO = OD  (Radii of the circle)

large therefore : : Delta AOBcong Delta COD: by: SSS SO,: angle 1=angle 2: by: CPCT.

Hence, eqyal chords subtend equal angles at the centre.

 

 

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