Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC. Is the given statement true or false and justify your answer

Solution:

Consider the figure

AB and AC are the two chords

Let us join OB and OC

In triangle OAB and triangle OAC

OA = OA (common side)

OC = OB (radius of circle)

It is not possible to prove that either a third side or any angle is equal and triangle OAB is not congruent to triangle OAC.

∠OAB ≠ ∠OAC

Therefore, the statement is false.

✦ Try This: Two chords PQ and PR of a circle with centre O are on the opposite sides of OP. Then ∠OPQ = ∠OPR. Is the given statement true or false and justify your answer

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 2

Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC. Is the given statement true or false and justify your answer

Summary:

The statement “Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC” is false

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