CBSE Class 10 Mathematics Standard 2024: question 9
Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.
Q9 · 1 mark · MCQCircles
Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:
- (A)4
- (B)3
- (C)2
- (D)1
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
Sketch two overlapping circles.
Hint 2
Check whether a tangent can pass between the circles.
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.
When two circles cut at two points, only the two direct (external) common tangents are possible.
- 1 mark
No transverse tangent can pass between them, because the circles overlap. So the maximum is 2, which is option (C).
Answer: 2, option (C)
Where the marks are
- States that 2 common tangents exist, option (C) (1 mark)
Revise the chapter
- Chapter: Circles (notes, formulas, where marks are lost and every past question)
More questions from Circles
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- 2024 board paper, set 30/3/1 (Standard), Q31 · 3 marksProve that the tangents drawn at the end points of a chord of a circle makes equal angles with the chord.
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.