Question

If AOB is a diameter of the circle and AC = BC, then $\angle CAB$ is equal to:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

We know that, diameter subtends a right angle to the circle.
$\angle BCA$ = ${90}^{\circ }$ ......(i)
AC = BC ......(ii)
$\Rightarrow$ $\angle ABC=\angle CAB$ [Angle opposite to equal sides are equal]

In $△$ ABC, $\angle CBA+\angle ABC+\angle BCA={180}^{\circ }$ [angle sum property of triangle]
$\angle CAB+\angle CAB+{90}^{\circ }={180}^{\circ }$
2 $\angle CAB={90}^{\circ }$
$\angle CAB={45}^{\circ }$