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Two equal chords AB and CD of a circle with centre O, intersect each other at point P inside the circle, prove that:

(i) AP = CP,

(ii) BP = DP

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Best answer

Drop OM and ON perpendicular on AB and CD.

Join OP, OB and OD.

∴ OM and ON bisect AB and CD respectively

(Perpendicular drawn from the centre of a circle to chord bisects it)

By Right Angle – Hypotenuse – Side criterion of congruence,

The corresponding parts of the congruent triangles are congruent.

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