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Question

O is any point on the bisector of the acute angle XYZ. From O, a line is extended to join XY such that OP is parallel to ZY. Then, YPO is:


A

Scalene

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B

Isosceles but not right angled

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C

Equilateral

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D

Right & isosceles

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Solution

The correct option is B

Isosceles but not right angled


POY = OYZ (alternate angles)

Y is bisected, so POY = PYO
Hence, PY = PO
So, YPO is isosceles

Also, it is given that XYZ is acute, so any angle which is half of it (bisected by OY) is less than 45.
or PYO + OYZ < 90

Hence, the third angle of the YPO i.e. YPO will be obtuse to satisfy angle-sum property of a triangle.

Hence, YPO is isosceles but not right angled.


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