Write True or False and justify your answer in each of the following:
Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB = \angle OAC$.
Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA$. Then $\angle OAB = \angle OAC$.
(B) The statement is False.
In $\triangle OAB$ and $\triangle OAC$,we have $OA = OA$ (common side) and $OB = OC$ (radii of the same circle).
However,the angles $\angle OAB$ and $\angle OAC$ are equal if and only if the chords $AB$ and $AC$ are equal in length $(AB = AC)$.
If the chords are of unequal lengths,the angles subtended by them at the center or the angles they make with the radius $OA$ will not be equal.
Therefore,the statement is not universally true.
In $\triangle OAB$ and $\triangle OAC$,we have $OA = OA$ (common side) and $OB = OC$ (radii of the same circle).
However,the angles $\angle OAB$ and $\angle OAC$ are equal if and only if the chords $AB$ and $AC$ are equal in length $(AB = AC)$.
If the chords are of unequal lengths,the angles subtended by them at the center or the angles they make with the radius $OA$ will not be equal.
Therefore,the statement is not universally true.
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