CBSE Class 10 Mathematics Standard 2025: question 7
Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.
Q7 · 1 mark · MCQCircles
In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If , then is :
- (A)
- (B)
- (C)
- (D)
Figure in the paper: A circle with centre O and horizontal diameter MN (M on the left, N on the right). Point L is on the upper part of the circle. Line RS is the tangent at L, with R on the upper-left side and S on the lower-right side. Chord LM is drawn. The angle at M between MN and ML is marked ; the angle at L between LR and LM is marked to be found. See it in the official paper.
Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.
Hints
Open one hint at a time and try again before the next.
Hint 1
Join O to L. What kind of triangle is OLM?
Hint 2
The radius OL is perpendicular to the tangent RS at L.
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.
- ½ mark
Join OL. Since (radii), .
- ½ mark
[tangent radius]. So . Option (B).
Answer: , option (B)
Where the marks are
- Uses the isosceles triangle OLM and tangent radius to get , option (B) (1 mark)
Revise the chapter
- Chapter: Circles (notes, formulas, where marks are lost and every past question)
- Topic: Tangent Perpendicular to Radius Theorem
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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.