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Tangents PA and PB from a… (Class 10 Maths Basic 2024, Q16)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2024: question 16

Set in the CBSE Class 10 board exam of 2024, paper 430/2/1, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQCircles

In the given figure, tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of . is equal to

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

Figure in the paper: A circle with centre O. External point P on the left with two tangents PA (upper) and PB (lower) touching the circle at A and B. The angle at P between the tangents is marked . Chord AB is drawn, joining A and B, and radius OB is drawn. The angle ABO (between chord BA and radius BO at B) 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 430/2/1.

Hints

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

Hint 1

Triangle PAB is isosceles.

Hint 2

Angle between radius OB and tangent PB is 90°.

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. so .

  2. [tangent ⟂ radius], so . Option (A).

    1 mark

Answer: , option (A)

Where the marks are

  • Uses equal tangents and radius ⟂ tangent to get 40° (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 430/2/1 (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.