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AB and CD are two chords of a… (Class 10 Maths 2024, Q11)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 11

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQTriangles

and are two chords of a circle intersecting at . Choose the correct statement from the following:

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

Figure in the paper: Circle with chords AB and CD intersecting at point P inside the circle. Points on the circle are labelled D (upper left), B (right), C (lower, near P) and A (bottom). Segments AD, AC, BC and the chord lines meet at P. The centre of the circle is marked with a dot but is not labelled. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Look for vertically opposite angles at P.

Hint 2

Angles subtending the same arc are equal; match the vertices in order.

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. In and : (vertically opposite), (angles in same segment on arc DB).

  2. By AA, (A↔C, D↔B, P↔P). Option (D).

    1 mark

Answer: △ADP ~ △CBP, option (D)

Where the marks are

  • Matches vertices correctly via AA similarity (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/2/1 (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.