Question

Draw a circle. Let AB be diameter. Let P is point on circle. Construct angle bisector of $\angle P$. The bisector_____.

• A. cuts diameter between B and centre
• B. cuts diameter between A and centre
• C. cuts diameter A and B at centre
  
• D. none

Answer 1

The correct option is D none

Suppose angle bisector of angle P cuts diameter AB at center.

Then in triangle AOP,

angle APO = 45 degree ( bisector of angle of semicircle ).

since triangle AOP is isosceles triangle.

So, PAO = 45 degree

So, angle AOP should be 90 degree, which is not necessary in all cases.

It depends upon the position of the point P.

Hence, correct answer is option D.