In the given figure, if PT is a tangent to a circle with centre O and ∠ TPO = 35°, then the measure of ∠ x is: (A) 110° (B) 115° (C) 120° (D) 125°

MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 10

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 10, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q10 · 1 mark · MCQCircles

In the given figure, if PT is a tangent to a circle with centre O and $∠ TPO = 3 5^{\circ}$ , then the measure of $∠ x$ is:

(A) $11 0^{\circ}$
(B) $11 5^{\circ}$
(C) $12 0^{\circ}$
(D) $12 5^{\circ}$

Figure in the paper: A circle with centre O. A tangent line touches the circle at T. P lies on the tangent outside the circle; a straight line from P passes through O and continues to the far side of the circle. TO is joined. The angle at P between PT and PO is marked $3 5^{\circ}$ . The angle at O between OT and the segment OX (going to the lower-left part of the circle) is marked $x$ . See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

The radius OT meets the tangent at a right angle.

Hint 2

Find $∠ T O P$ first, then use the straight line through P and O.

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.

$∠ O T P = 9 0^{\circ}$ [tangent ⟂ radius].
In $△ O T P$ : $∠ T O P = 18 0^{\circ} - 9 0^{\circ} - 3 5^{\circ} = 5 5^{\circ}$ .
Angle $x$ and $∠ T O P$ form a linear pair on line PO, so $x = 18 0^{\circ} - 5 5^{\circ} = 12 5^{\circ}$ . This is option (D).
1 mark

Answer: $12 5^{\circ}$ , option (D)

Where the marks are

Uses tangent ⟂ radius and the linear pair to get $12 5^{\circ}$ , option (D) (1 mark)

Revise the chapter

Chapter: Circles (notes, formulas, where marks are lost and every past question)
Topic: Tangent Perpendicular to Radius Theorem

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 30/3/1 (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.

CBSE Class 10 Mathematics Standard 2024: question 10

Hints

Step-by-step solution

Revise the chapter

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