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RJ and RL are two tangents to… (Class 10 Maths 2024, Q16)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 16

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQCircles

In the given figure, RJ and RL are two tangents to the circle. If , then the measure of is :

  1. (A)
  2. (B)
  3. (C)
  4. (D)

Figure in the paper: A circle with centre O. Two tangents RJ and RL meet at external point R, touching the circle at J and L. Chord JL is drawn; the angle RJL = 42° is marked at J. OJ and OL are radii joined to O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Triangle RJL is isosceles.

Hint 2

∠JOL and ∠JRL are supplementary.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. RJ = RL [tangents from external point], so and .

  2. In quadrilateral OJRL, [tangent ⟂ radius], so , option (B).

    1 mark

Answer: , option (B)

Where the marks are

  • Uses equal tangents and tangent ⟂ radius to get 84° (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Circles, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/5/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.