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PQ is tangent to the circle… (Class 10 Maths 2023, Q5)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 5

Set in the CBSE Class 10 board exam of 2023, paper 30/1/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 1 mark · MCQCircles

In the given figure, PQ is tangent to the circle centred at O. If , then the measure of will be

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

Figure in the paper: A circle with centre O. Chord AB is drawn; angle AOB = 95° is marked at O. A line PQ touches the circle at B; P is on one side of B and Q on the other, with ray BP going up-right and BQ going down-left. Angle ABQ is marked at B. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/1/1.

Hints

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

Hint 1

Triangle AOB is isosceles.

Hint 2

The radius OB is perpendicular to the tangent PQ at B.

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. In , (radii), so .

  2. [tangent ⟂ radius at the point of contact].

  3. . Option (A).

    1 mark

Answer: 47.5°, option (A)

Where the marks are

  • Finds , uses tangent ⟂ radius and gets , option (A) (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 paper2023 board paper, set 30/1/1 (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.