Q1. [2] § 10.1 Introduction § 10.2 Tangent to a Circle § 10.4 Summary
In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If $\angle BAC = 65°$, then find the measure of $\angle BOC$.
Previously asked in CBSE board exam
2023 30/2/1 Q25
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
In quadrilateral ABOC:
$$\angle OBA = \angle OCA = 90°$$
(radius is perpendicular to tangent at point of contact)
Sum of angles of a quadrilateral = 360°
$$\angle BAC + \angle OBA + \angle BOC + \angle OCA = 360°$$
$$65° + 90° + \angle BOC + 90° = 360°$$
$$\angle BOC = 360° - 245° = \boxed{115°}$$
Source: Chapter 10, Section 10.2 (Theorem 10.1)
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Explanation
- The key property used: tangent ⊥ radius at point of contact, so ∠OBA = ∠OCA = 90°.
- Since ABOC is a quadrilateral, all four angles sum to 360°.
- This is a standard 2-mark question: state the property (1 mark) and show the calculation leading to the answer (1 mark).
- A common mistake is using the wrong relationship (e.g., saying ∠BOC = 180° − ∠BAC = 115°, which gives the same answer but must be justified properly via the quadrilateral angle sum).
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cbse.gov.in.