Mathematics
If P is a point on a circle with centre O. If P is equidistant from the two radii OA and OB, prove that arc AP = arc PB.
Circles
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Answer
In △ OMP and △ ONP,
⇒ ∠OMP = ∠ONP = 90°
⇒ OP = OP (Hypotenuse)
⇒ PM = PN (Given)
∴ △ OMP ≅ △ ONP
Since, the triangles are congruent, their corresponding parts are equal.
∠MOP = ∠NOP
∠AOP = ∠BOP
Equal angles at the centre of a circle subtend equal arcs.
∴ arc AP = arc PB.
Hence, proved that arc AP = arc PB.
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