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PA and PB are tangents from… (Class 10 Maths 2023, Q14)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 14

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section A, question 14, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q14 · 1 mark · MCQCircles

In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle. Then the measure of is

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

Figure in the paper: Circle with centre C. External point P on the left with tangents PA (touching at top point A) and PB (touching at bottom point B). Angle APB = 55° marked at P. Point Q is on the right side of the circle; chords QA and QB are drawn and angle AQB is marked at Q. Radii CA and CB are drawn. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

The angle between the tangents and the angle at the centre are supplementary.

Hint 2

How is the angle at the centre related to the angle at Q on the circle?

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].

  2. [angle at the centre is twice the angle at the circumference]. Option (A).

    1 mark

Answer: 62½°, option (A)

Where the marks are

  • Finds ∠ACB = 125° and halves it to get ∠AQB = 62½° (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 30/6/1 (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.