CBSE Class 10 Mathematics Standard sample paper 2025-26: question 18
From the official CBSE sample question paper for 2025-26, section A, question 18, for 1 mark. Try it first; the hints and our step-by-step solution are below.
Q18 · 1 mark · MCQCircles
The length of a tangent drawn to a circle of radius 9 cm from a point at a distance of 41cm from the centre of the circle is
- (A)40cm
- (B)9cm
- (C)41cm
- (D)50cm
Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.
Hints
Open one hint at a time and try again before the next.
Hint 1
Join the centre to the point of contact. What angle is formed?
Hint 2
Apply Pythagoras' theorem in the right triangle.
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.
The tangent is perpendicular to the radius at the point of contact T, so triangle OTP is right-angled at T.
- 1 mark
cm. The answer is option (A).
Answer: 40 cm, option (A)
Where the marks are
- Uses tangent ⟂ radius and Pythagoras to get 40 cm, option (A) (1 mark)
Revise the chapter
- Chapter: Circles (notes, formulas, where marks are lost and every past question)
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