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PA is a tangent to a… (Class 10 Maths Basic 2025, Q9)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 9

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQCircles

In the given figure, PA is a tangent to a circle with centre O. If OP = 10 cm, then the length of AP is :

  1. (A) cm
  2. (B)20 cm
  3. (C)5 cm
  4. (D) cm

Figure in the paper: Circle with centre O; P outside the circle; PA is a tangent touching the circle at A. OA is a radius. Angle APO = 30°. OP = 10 cm is marked along the line from O to P. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

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

Hint 2

In the right triangle, OP is the hypotenuse and AP is the side next to the 30° angle.

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 at the point of contact].

  2. In right : , so cm. The answer is option (D).

    1 mark

Answer: 5√3 cm, option (D)

Where the marks are

  • Uses ∠OAP = 90° and cos 30° to get AP = 5√3 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 paper2025 board paper, set 430/1/1 (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.