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From a point P, two… (Class 10 Maths Basic 2023, Q5)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 5

Set in the CBSE Class 10 board exam of 2023, paper 430/2/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 1 mark · MCQCircles

From a point P, two tangents PQ and PR are drawn to a circle with centre at O. T is a point on the major arc QR of the circle. If , then equals:

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

Figure in the paper: Circle with centre O. External point P with tangents PQ and PR touching the circle at Q and R. Radii OQ and OR are drawn. T is a point on the major arc QR on the left side; chords TQ and TR are drawn. The angle at P, QPR, is marked . See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/2/1.

Hints

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

Hint 1

The radius is perpendicular to the tangent at the point of contact.

Hint 2

Find from quadrilateral OQPR, then use the angle at the centre theorem.

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 in quadrilateral OQPR, .

  2. Angle subtended at the circumference is half the angle at the centre: . Option (C).

    1 mark

Answer: , option (C)

Where the marks are

  • Finds and halves it to get (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 paper2023 board paper, set 430/2/1 (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.