If two chords of a circle are equally inclined to the the diameter through their point of intersection ,prove that the chords are equal

given: AB is the diameter of the circle with center O.



construction; draw OM⊥AC and ON⊥AD


in the triangle OMA and triangle ONA,

∠OMA=∠ONA=90 deg (by the construction)


OA is common.

therefore by AAS congruency, triangles are congruent.

hence by the congruent property of the triangles OM = ON

⇒AC = AD [equal chords are equidistant from center ]

which is the required result.

hope this helps you.


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