Q1. [1] § 10.2 Tangent to a Circle § 10.4 Summary
In the given figure, PQ and PR are tangents to a circle with centre O and radius 3 cm. If $\angle QPR = 60°$, then the length of each tangent is :
- A $3\sqrt{3}$ cm
- B $3$ cm
- C $6$ cm
- D $\sqrt{3}$ cm
Previously asked in CBSE board exam
2026 30/3/1 Q2
Generated by claude-sonnet-4-6 · 2026-06-15 10:26 · grounding rag
Model Answer
Option (A) $3\sqrt{3}$ cm
Since OQ ⊥ PQ (radius ⊥ tangent), in right △OQP: ∠OQP = 90°, ∠QPR = 60° ⟹ ∠QPO = 30°.
So tan 30° = OQ/PQ ⟹ 1/√3 = 3/PQ ⟹ PQ = 3√3 cm.
Explanation
- The key property used: radius ⊥ tangent at point of contact (Theorem 10.1).
- Since OP bisects ∠QPR (Theorem 10.2 Remark), ∠QPO = 30°.
- Apply tan 30° = opposite/adjacent = OQ/PQ in right △OQP.
- Many students mistakenly use sin or cos; here tan is direct since OQ (radius) and PQ (tangent) are the two legs.
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