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In the given figure, $△ XYZ$ is inscribed in a circle with centre $O$ . If the length of chord $YZ$ is equal to the radius of the circle $OY$ , then $∠ YXZ$ is equal to

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60^{o}

30^{o}

80^{o}

100^{o}

answer is B.

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Detailed Solution

Consider the given question,
Question Image

Here,

OY = OZ = radius = r

Given,

YZ = r

⟹ △ OYZ

is equilateral

⟹ ∠ YOZ = 60^{\circ}

We know that,
Angle made by a chord on any point on the circle is half the angle made by the chord at the center.
Then,

⟹ ∠ YXZ = \frac{∠ YOZ}{2}

⟹ ∠ YXZ = \frac{60 °}{2} = 30^{\circ}

Hence, the value of

∠ YXZ

30^{\circ}

.
Therefore, option 2 is correct.

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