8
Question
Angles subtended by equal chords at the centre of the circle are
Angles subtended by equal chords at the centre of the circle are
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Solution
The correct option is B equal
Consider the above diagram of a circle with centre O.
PQ and RS are equal chords of the circle.
The angle subtended by chord PQ at the center of circle is ∠POQ.
The angle subtended by chord RS at the center of circle is ∠ROS.
In △s POQ and ROS, we have
PQ = RS (Given)
OP = OR (Radii of the same circle), and
OQ = OS.
Thus, by SSS congruency criterion, △POQ=△ROS.
By C.P.C.T., ∠POQ=∠ROS.
Consider the above diagram of a circle with centre O. PQ and RS are equal chords of the circle.
The angle subtended by chord PQ at the center of circle is ∠POQ.
The angle subtended by chord RS at the center of circle is ∠ROS.
In △s POQ and ROS, we have
PQ = RS (Given)
OP = OR (Radii of the same circle), and
OQ = OS.
Thus, by SSS congruency criterion, △POQ=△ROS.
By C.P.C.T., ∠POQ=∠ROS.
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