Q1. [1] § 10.2 Tangent to a Circle § 10.3 Number of Tangents from a Point on a Circle § 10.4 Summary
In the given figure, $AB$ and $AC$ are tangents to the circle. If $\angle ABC = 42°$, then the measure of $\angle BAC$ is :
- A 96°
- B 42°
- C 106°
- D 86°
Previously asked in CBSE board exam
2024 30/4/1 Q15
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
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.
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