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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.

Answers (1)

False

Solution:

Given:

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

They are given to be at the opposite sides of OA.

To find out

If \angleOAB =\angleOAC

Join OB and OC

Consider \triangleAOC & \triangleAOB we have

OB = OC  (Radii of the same circle)

AO = AO  (common)

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

Also, we do not have any other condition to prove that the triangles are congruent.

\therefore  \angleOAB \neq  \angleOAC

Therefore the given statement is false.

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