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AB is diameter of the… (Class 10 Maths Basic 2025, Q5)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2025: question 5

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section A, question 5, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q5 · 1 mark · MCQCircles

In the given figure, AB is diameter of the circle with centre O. CD is tangent to the circle so that . The value of is

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

Figure in the paper: Circle with centre O and diameter AB (A at top, B at bottom). Point C lies on the circle on the right; O is joined to C by a dashed line. Line segment CD is a tangent at C, with D above C. Chord AC is drawn and the angle ACD = 40° is marked between chord CA and tangent CD. Chord BC is also drawn. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

The radius OC is perpendicular to the tangent.

Hint 2

Angle ACB is in a semicircle.

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 ; gives .

  2. [angle in semicircle], so . Option (B).

    1 mark

Answer: , option (B)

Where the marks are

  • Uses tangent–radius and semicircle angle 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 paper2025 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.