In the given figure, $AB$ and $AC$ are tangents to the circle. If $\angle ABC = 42°$, then the measure of $\a…

Question

In the given figure, $AB$ and $AC$ are tangents to the circle. If $\angle ABC = 42°$, then the measure of $\angle BAC$ is :

Accepted Answer

## Model Answer Since AB and AC are tangents from external point A, triangle ABC is isosceles with AB = AC, so ∠ACB = ∠ABC = 42°. ∠BAC = 180° − 42° − 42° = **96°**. → Option **A** ## Explanation Equal tangents from an external point (Theorem 10.2) make △ABC isosceles, so base angles ∠ABC = ∠ACB = 42°. Apply angle sum: 180° − 84° = 96°. Watch for this standard isosceles-tangent triangle setup in MCQs.

Mathematics — CBSE Class 10 board question