Two chords AB and AC of a circle with center O are on the opposite sides of OA. Then OAB = OAC.

Question

Philoid · Accepted Answer

FALSE

Let AB and AC be the chord of the circle with center O on the opposite side of OA.

Consider the triangles AOC and AOB:

AO = AO (Common side in both triangles)

OB = OC (Both OB and OC are radius of circle)

But we can’t show that either the third side of both triangles are equal or any angle is equal. Therefore ΔAOB is not congruent to ΔAOC.

∴ ∠OAB ≠ ∠OAC.