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Directions: In Q. No. 19… (Class 10 Maths Basic 2024, Q19)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/1/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2024: question 19

Set in the CBSE Class 10 board exam of 2024, paper 430/1/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedCircles

Directions: In Q. No. 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Select the correct option from the following options.

Assertion (A): If the PA and PB are tangents drawn to a circle with centre O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.

Reason (R): In a cyclic quadrilateral, opposite angles are equal.

  1. (A)Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.
  2. (B)Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain Assertion (A).
  3. (C)Assertion (A) is true but Reason (R) is false.
  4. (D)Assertion (A) is false but Reason (R) is true.

Figure in the paper: Circle with centre O. Two tangents from external point P touch the circle at A (upper) and B (lower). Radii OA and OB are drawn, forming quadrilateral OAPB with P on the right. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/1/1.

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

Check: are opposite angles of a cyclic quadrilateral equal or supplementary?

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 ; opposite angles supplementary ⇒ OAPB is cyclic. A is true.

  2. In a cyclic quadrilateral opposite angles are supplementary, not necessarily equal, so R is false. Option (C).

    1 mark

Answer: Option (C)

Where the marks are

  • A true via supplementary opposite angles, R false (1 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 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.