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Question
PQ and RS are two equal chords of a circle with centre O such that ∠POQ = 70°, then ∠ORS =
Options
60°
70°
55°
80°
MCQ
Solution
55°
Explanation;
Hint:
∠POQ = 70° ...(Vertically opposite Angle)
∠ORS and ∠OSR are equal ...(OR = OS radius of the circle)
∠ORS + ∠OSR + ∠ROS = 180°
x° + x° + 70° = 180°
2x + 70° = 180°
2x = 180° – 70° = 110°
x = `(110^circ)/2` = 55°
∴ ∠ORS = 55°
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Converse: If the angles subtended by two chords at the centre of a circle are equal, then the chords are equal.
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