$O$ is the point on the bisector of an acute angle $∠ X Y Z$ . If $O P$ is parallel to $Z Y$ Then, $△ Y P O$ is:

Scalene

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Isosceles but not right angled

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Equilateral

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Right-angled & isosceles

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Solution

The correct option is B Isosceles but not right angled
$O Y$ bisects $∠ X Y Z$
Hence, $∠ P Y O = ∠ O Y Z$ (1)
Now, $P O ∥ Y Z$
Hence, $∠ O Y Z = ∠ P O Y$ (Alternate angles) (2)
Thus, from (1) and (2), we have
$∠ P Y O = ∠ P O Y$
$△ P O Y$ is an Isosceles triangle but not a right-angled triangle.

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