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AP and AQ are tangents… (Class 10 Maths Basic 2024, Q16)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2024: question 16

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQCircles

AP and AQ are tangents drawn from an external point A to a circle with centre O and inclined to each other at an angle of . If the length of each tangent is 2 cm, then the radius of the circle is :

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

Figure in the paper: Circle with centre O. External point A on the left with two tangent segments AP and AQ, each labelled 2 cm. P and Q are the points of contact on the circle; the angle at A is marked . Radii OP and OQ are drawn to the points of contact, and O is joined to the circle's centre. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

What angle does a radius make with the tangent at the point of contact?

Hint 2

All four angles of APOQ are and adjacent sides AP, AQ are equal.

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 APOQ, , [tangent ⟂ radius], so and APOQ is a rectangle with , i.e. a square.

  2. Hence radius cm.

    1 mark

Answer: 2 cm, option (B)

Where the marks are

  • Recognises APOQ as a square, radius = 2 cm (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 430/5/1 (Basic): 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.