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Question
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
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Solution
Given:
In the figure, O is centre of the circle and PQ is a chord.
OM ⊥ PQ
To prove: PM = QM
Construction: Join Op and OQ
Proof:
In right triangles ΔOPM and ΔOQM,
OP = OQ ....[radii of the same circle]
OM = OM ....[common]
∴ By right angle-Hypotenuse-Side criterion of congruency,
ΔOPM ≅ΔOQM
The corresponding parts of the congruent triangles are congruent.
∴ PM = QM.
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