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TA is a tangent to the circle… (Class 10 Maths 2023, Q15)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 15

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section A, question 15, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q15 · 1 mark · MCQCircles

In the given figure, TA is a tangent to the circle with centre O such that OT = 4 cm, , then length of TA is:

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

Figure in the paper: A circle with centre O. T is a point outside the circle on a horizontal line; TA is a tangent touching the circle at A. The segment OT is marked 4 cm, and the angle at T between TO and TA is . See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

The radius OA is perpendicular to the tangent TA.

Hint 2

In right triangle OAT, OT is the hypotenuse. Use .

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 is right-angled at A.

  2. .

  3. cm. So the answer is option (A).

    1 mark

Answer: cm, option (A)

Where the marks are

  • Chooses option (A) cm (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 paper2023 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.