Question

In figure, AOB is a diameter of the circle and $AC=BC.Then\angle CAB$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Given in figure, AB is a diameter of a circle is AB

Diameter of circle subtends a right angle at point on circumference of the circle.

AB subtends ${90}^{\circ }$ angle at the circumference

So, $\angle ACB={90}^{\circ }$

$AC=BC$ (given)

Therefore triangle $\angle CAB$ is isosceles right triangle.

$\therefore \angle CAB={45}^{\circ }$

So, option B will be the answer.