Question 11

State True or False. In a triangle $$ABC$$ if the internal and external bisectors of angle $$A$$ meet the circum circle at $$X$$ and $$Y$$ then $$XY$$ is a diameter of the circum circle.


Correct Answer: True

Solution

The internal and external bisectors of an angle are perpendicular, so $$\angle XAY = 90^\circ$$. An inscribed right angle stands on a diameter, so $$XY$$ is a diameter of the circumcircle. The statement is True.

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