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Area of a Circle

In the given ...

Question

In the given figure, $Δ X Y Z$ is inscribed in a circle with centre O. If the length of chord YZ is equal to the radius of the circle OY then $∠ Y X Z$ =

60^{o}

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30^{o}

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80^{o}

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100^{o}

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Solution

The correct option is B $30^{o}$
$G i v e n - O i s t h e c e n t r e o f a c i r c l e i n w h i c h Δ X Y Z h a s b e e n i n s c r i b e d . T h e r a d i u s O Y = Y Z . T o f i n d o u t - ∠ Y X Z = ? S o l u t i o n - I n Δ O Y Z O Y = O Z (r a d i i o f t h e s a m e c i r c l e) . B u t O Y = Y Z . ∴ O Y = O Z = Y Z . S o Δ O Y Z i s e q u i a n g u l a r . ∴ E a c h a n g l e = 60^{o} . S o ∠ Y O Z = 60^{o} . N o w t h e c h o r d Y Z s u b t e n d s ∠ Y O Z t o t h e c e n t r e a n d ∠ Y X Z t o t h e c i r c u m f e r e n c e a t X . ∴ ∠ Y X Z = \frac{1}{2} ∠ Y O Z = \frac{1}{2} \times 60^{o} = 30^{o} . A n s - O p t i o n B .$

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△ X Y Z

O

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O Y

∠ Y X Z

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A B C D

O

A C

∠ B A C = 30^{o}

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