Question

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

Answer 1

Given: Two chords AB and AC of a circle C(O, r), such that AB and AC are equally inclined to diameter AOD.

To prove: AB = AC

Construction : Draw OL perpendicular to AB and OM perpendicular to AC.

Proof:

In $\Delta OLA$ and $\Delta OMA$,

$\angle OLA=\angle OMA={90}^{\circ }$

$OA=OA$ [Common]

$\angle OAL=\angle OAM$ [Given]

$\Delta OLA\cong \Delta OMA$ (RHS congruence condition)

$OL=OM$ (CPCT)

Chords AB and AC are equidistant form O

$\therefore AB=AC$