Q1. [1] § 10.1 Introduction § 10.2 Tangent to a Circle
In the adjoining figure, PA and PB are tangents to a circle with centre O. The measure of angle APB is
- A 210°
- B 150°
- C 105°
- D 30°
Previously asked in CBSE board exam
2025 30/5/1 Q11
Generated by claude-sonnet-4-6 · 2026-06-15 10:26 · grounding rag
Model Answer
Answer: (D) 30°
Reflex ∠AOB = 210°, so ∠AOB (minor) = 360° − 210° = 150°.
Since OA ⊥ PA and OB ⊥ PB, in quadrilateral OAPB: ∠APB = 360° − 90° − 90° − 150° = 30°.
Explanation
- The reflex angle given (210°) is the major arc angle; the actual ∠AOB = 360° − 210° = 150°.
- Tangent ⊥ radius gives ∠OAP = ∠OBP = 90°.
- Sum of angles in quadrilateral OAPB = 360°, so ∠APB = 360° − 90° − 90° − 150° = 30°.
- A common mistake is using 210° directly — always convert the reflex angle first.
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