Question

Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB=\angle OAC.$ . Write True or False and justify your answer

Answer 1

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

From the triangles $AOC$ and $AOB$:

$AO=AO$ (Common side in both triangles)

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

But we can’t determine that either the third side of both triangles is equal or any angle is equal.

Therefore $△AOB$ is not congruent to $∆AOC$.

∴ $\angle OAB\ne \angle OAC$.

Hence, the given statement is false.