Question

In the given figure $\angle ABC={38}^{\circ },$ then $\angle BAC$ is equal to

• A. ${74}^{\circ }$
• B. ${76}^{\circ }$
• C. ${38}^{\circ }$
• D. ${36}^{\circ }$

Answer 1

The correct option is B ${76}^{\circ }$

From tangent secant theorem, angle in an alternate segment are equal, So $\angle ABC=\angle BEA={38}^{\circ }$
Now, the angle made by chord AB at the centre is double the angle made by chord at circumference,
hence, $\angle BOA=2\angle BEA$
$\angle BOA=2\times {38}^{\circ }$
$\angle BOA={76}^{\circ }$