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.