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State true or false.

If in the given figure, AB and AC are two equal chords of the circle with centre O, and then O lies on the bisectors of ∠BAC.

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True

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answer is A.

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Detailed Solution

It is given that AB and AC are two equal chords of the circle with centre O.
Question Image

We have to check if O lies on the bisectors of ∠BAC.
In ∆AOB and ∆AOC,
OA=OA    (Common side)
OB=OC      (radius of the circle)
AB=AC    (given)

∴ △ A O B ≅ △ O A C

[By SSS Congruency rule]
So,

∠ O A C = ∠ O A B

(c.p.c.t)
Hence, O lies on the bisector of

∠ B A C

.
Thus, the statement is true.
Therefore, option 1 is correct.

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