Question

Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then:

• A. $\angle OAB=\angle OAC$.
• B. $\angle OAB\ne \angle OAC$.
• C. Cannot be determined
• D. None of the above

Answer 1

Answer: (B)

Given-

$AB$ & $AC$ are chords of a circle with centre O.

They are to the opposite sides of OA.

To find out-

If $\angle OAB=\angle OAC.$

Solution-

$OB$ & $OC$ are joined.

Between $\Delta AOC$ & $\Delta AOB$ we have,

$OB=OC$ .....(radii of the same circle).

But it is not sure whether $AB=AC$ or not.

So, we cannot have SSS test for the congruency of the triangles.

$\therefore \angle OAB\ne \angle OAC$.