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O is the centre of the circle… (Class 10 Maths 2024, Q18)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 18

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 18, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q18 · 1 mark · MCQCircles

In the given figure, O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of with MN. The measure of is:

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

Figure in the paper: A circle with centre O. Chord MN is drawn. Radii OM and ON are joined forming triangle OMN. A tangent line through M extends to point L on one side. The angle between the tangent ML and chord MN at M is marked . See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

The radius OM is perpendicular to the tangent ML.

Hint 2

Triangle OMN is isosceles.

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. [tangent ⟂ radius], so .

  2. OM = ON (radii), so . Then , which is option (B).

    1 mark

Answer: , option (B)

Where the marks are

  • Uses tangent ⟂ radius and the isosceles triangle to get , option (B) (1 mark)

Revise the chapter

  • Chapter: Circles (notes, formulas, where marks are lost and every past question)
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 30/3/1 (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.