Q1. [1]
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.
If a question refers to an image, map, graph or diagram that is not shown here, open the Study Guide single page app, go to
Library and find the actual CBSE question paper. The original papers are also available on the CBSE website:
cbse.gov.in.