Question

The angle subtended by a diameter at any point on the circumference of the circle is

• A. ${90}^{\circ }$
• B. ${180}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

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

Arc $\text{AB}$ makes ${180}^{\circ }$ at the center $\text{O}$ of the circle where $\text{AB}$ is the diameter of the circle.
i.e. $\angle \text{AOB}={180}^{\circ }$
So, the angle subtended by the arc $\text{AB}$ where $\text{AB}$ is the diameter, at any point of the cricumeference of the circle will be half of $\angle \text{AOB}$
i.e. $\angle \text{APB}=\frac{\angle \text{AOB}}{2}$
$=\frac{{180}^{\circ }}{2}$
$={90}^{\circ }$