Question

AB is the longest chord of a circle with centre O and P is a point on it, not coinciding with A or B. Then $\angle APB=$

• A. ${60}^{\circ }$
• B. ${90}^{\circ }$
• C. ${45}^{\circ }$

Answer 1

The correct option is B ${90}^{\circ }$


Consider the circle as shown, with centre O and AB as the longest chord. Since diameter is the longest chord, AB is the diameter.
Recall that the angle subtended by the Diameter at a point on the circle is ${90}^{\circ }$.
Therefore $\angle APB={90}^{\circ }$