Question

The two chord CA and CB are equidistant from the center O. Find the angle ∠B.
degrees

Answer 1

In the given figure, AB is the diameter.
Hence it will subtend ${90}^o$ at C.
$\therefore \angle C={90}^o$

Given: CA and CB are equidistant from the center.
$\therefore$ The measure of AC and CB are same.

Hence, the measure of opposite angles are same, i.e., $\angle A=\angle B.$

From the interior angle sum property of the triangle,
$\angle A+\angle B+\angle C={180}^o$
$\Rightarrow 2\times \angle B={180}^o-{90}^o$
$\Rightarrow \angle B={45}^o$