Q1. [1] § 10.2 Tangent to a Circle § 10.3 Number of Tangents from a Point on a Circle § 10.4 Summary
In the adjoining figure, TS is a tangent to a circle with centre O. The value of $2x°$ is
- A 22.5
- B 45
- C 67.5
- D 90
Previously asked in CBSE board exam
2025 30/6/1 Q11
Generated by claude-sonnet-4-6 · 2026-06-15 10:26 · grounding rag
Model Answer
In △OTS: ∠OST = 90° (radius ⊥ tangent), so 3x° + x° + 90° = 180° → 4x = 90° → x = 22.5°. Therefore, 2x° = 45°.
Option B
Explanation
Since OS is a radius and TS is a tangent, ∠OST = 90° (Theorem 10.1). The angles of △OTS sum to 180°: 3x + x + 90 = 180 → x = 22.5, so 2x = 45. Always apply the radius-tangent perpendicularity property first in such problems.
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