CBSE Class 10 Mathematics Standard sample paper 2024-25: question 7
From the official CBSE sample question paper for 2024-25, 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, a tangent has been drawn at a point P on the circle centred at O. If then is equal to
- (A)
- (B)
- (C)
- (D)
Figure in the paper: A circle with centre O. A point P lies on the circle; a tangent line passes through P, with T on the tangent on the left of P and an arrow on the right. Q is another point on the circle, joined to P by a chord. O is joined to P and to Q by radii. The angle TPQ is marked between the tangent (toward T) and chord PQ. See it in the official paper.
Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.
Hints
Open one hint at a time and try again before the next.
Hint 1
What angle does the radius make with the tangent at ?
Hint 2
Triangle has two equal sides.
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.
[tangent ⟂ radius]. So .
- 1 mark
[radii], so . Then . The answer is option (C).
Answer: , option (C)
Where the marks are
- Uses tangent ⟂ radius and the isosceles triangle to get (1 mark)
Revise the chapter
- Chapter: Circles (notes, formulas, where marks are lost and every past question)
- Topic: Tangent Perpendicular to Radius Theorem
More questions from Circles
- 2024 board paper, set 30/2/1 (Standard), Q17 · 1 markIn the given figure, AT is tangent to a circle centred at O. If ∠ CAT = 40°, then ∠ CBA is equal to
- 2024 board paper, set 30/3/1 (Standard), Q10 · 1 markIn the given figure, if PT is a tangent to a circle with centre O and ∠ TPO = 35°, then the measure of ∠ x is:
- 2023 board paper, set 30/4/1 (Standard), Q14 · 1 markIn the given figure, PQ is a tangent to the circle with centre O. If ∠ OPQ = x, ∠ POQ = y, then x + y is:
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.