Q1. [1] § 10.2 Tangent to a Circle § 10.3 Number of Tangents from a Point on a Circle § 10.4 Summary
In the given figure, RJ and RL are two tangents to the circle. If $\angle RJL = 42°$, then the measure of $\angle JOL$ is :
- A $42°$
- B $84°$
- C $96°$
- D $138°$
Previously asked in CBSE board exam
2024 30/5/1 Q16
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
(C) 96°
Since RJ = RL (tangents from external point), △RJL is isosceles, so ∠RLJ = ∠RJL = 42°. Thus ∠JRL = 180° − 84° = 96°. Since ∠JOL + ∠JRL = 180° (tangent ⊥ radius makes ROJL a cyclic quadrilateral with two right angles), ∠JOL = 96°.
Explanation
In quadrilateral RJOL: ∠OJR = ∠OLR = 90° (tangent ⊥ radius). So ∠JOL + ∠JRL = 180°. Find ∠JRL using the isosceles triangle property (RJ = RL), then subtract from 180°. Examiners expect you to recall that the angle at centre and angle at external point are supplementary.
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