Q1. [1] § 10.1 Introduction § 10.2 Tangent to a Circle
In the given figure, PQ is tangent to the circle centred at O. If $\angle AOB = 95°$, then the measure of $\angle ABQ$ will be
- A 47.5°
- B 42.5°
- C 85°
- D 95°
Previously asked in CBSE board exam
2023 30/1/1 Q5
Generated by claude-sonnet-4-6 · 2026-06-15 10:27 · grounding rag
Model Answer
Option (A) 47.5°
OB ⊥ BQ (radius ⊥ tangent), so ∠OBQ = 90°. In △OAB, OA = OB (radii), so ∠OAB = ∠OBA = (180° − 95°)/2 = 42.5°. Therefore, ∠ABQ = 90° − 42.5° = 47.5°.
Explanation
Key steps: (1) Tangent ⊥ radius at point of contact gives ∠OBQ = 90°. (2) Since OA = OB (radii), △OAB is isosceles, so ∠OBA = (180° − 95°)/2 = 42.5°. (3) ∠ABQ = ∠OBQ − ∠OBA = 90° − 42.5° = 47.5°. Examiners expect both the tangent-radius perpendicularity theorem and the isosceles triangle property to be applied.
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