Skip to content

O is the centre of the circle… (Class 10 Maths 2024, Q24)

questionbuddy.in/q/cbse-10-maths-2024-30-4-1-q24-centre-circle-value

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 24

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerCircles

In the given figure, O is the centre of the circle. If , then find the value of .

Figure in the paper: A circle with centre O. Chord AB is drawn with the central angle AOB marked as 145 degrees. A point C lies on the circle on the arc opposite to the major side near the bottom, and the angle ACB is marked as x, with segments CA and CB drawn. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

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

Hint 1

C lies on the minor arc, so x is not simply half of 145°.

Hint 2

Take a point on the major arc and use the angle at the centre theorem, then a cyclic quadrilateral property.

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. Take a point P on the major arc AB and join PA and PB.

    ½ mark

  2. [angle at the centre is double the angle at the remaining part of the circle]

    ½ mark

  3. APBC is a cyclic quadrilateral, so [opposite angles of a cyclic quadrilateral are supplementary]

    ½ mark

  4. , so .

    ½ mark

Answer: x = 107.5°

Where the marks are

  • Takes a point P on the major arc and joins AP, BP (½ mark)
  • ∠APB = 72.5° (½ mark)
  • Uses ∠APB + ∠ACB = 180° (½ mark)
  • x = 107.5° (½ mark)

Revise the chapter

  • Chapter: Circles (notes, formulas, where marks are lost and every past question)
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 30/4/1 (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.