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

QUESTION

 In the given figure, O is the centre of the circle, AM = PQ, AQ is a straight line and $\angle AOM=85^o.$  The measure of $\angle MOP$ is

 OPTIONS A. $85^o$ B. $10^o$ C. $20^o$ D. $42.5^o$
Right Option : B

EXPLANATION
Explain TypeExplanation Content
Text

As AM= PQ

Equal Chord subtend equal angle at the centre

$\angle POQ=\angle AOM=85^o.$

AS AQ is a straight line

$\angle QOP+ \angle MOP + \angle MOA=180^o.$

$85^0+ \angle MOP + 85^0=180^o.$

$170^0+ \angle MOP =180^o.$

$\angle MOP =10^o.$

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