Exercise 10.1, Question 1
How many tangents can a circle have?
Show solution
- There is one tangent at each point of the circle, and a circle has infinitely many points.
Answer: Infinitely many
NCERT Solutions for Class 10 Maths Chapter 10 Exercise 10.1
Exercise 10.1: Tangents and secants. A tangent meets the circle at exactly one point (the point of contact); a secant meets it at two. Through each point of the circle there is exactly one tangent, so a circle has infinitely many tangents, and at most two of them are parallel to a given line.
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Exercise 10.1 questions and solutions
Exercise 10.1, Question 2
Fill in the blanks.
(i) A tangent to a circle meets it in ____ point(s).
Show solution
- By definition a tangent touches the circle once.
Answer: one
(ii) A line meeting a circle in two points is a ____.
Show solution
- It cuts through the circle.
Answer: secant
(iii) A circle can have ____ parallel tangents at most.
Show solution
- Parallel tangents touch at the two ends of a diameter perpendicular to them.
Answer: two
(iv) The common point of a tangent and a circle is the ____.
Show solution
- It is where the tangent touches.
Answer: point of contact
Exercise 10.1, Question 3
A tangent PQ at P to a circle of radius 5 cm meets a line through the centre O at Q, with \(OQ = 12\) cm. PQ = (A) 12 cm (B) 13 cm (C) 8.5 cm (D) \(\sqrt{119}\) cm
Show solution
- \(OP \perp PQ\), so \(PQ^2 = OQ^2 - OP^2 = 144 - 25 = 119\).
Answer: (D) \(\sqrt{119}\) cm
Exercise 10.1, Question 4
Draw a circle and two lines parallel to a given line, one a tangent and the other a secant.
Show solution
- Draw the diameter perpendicular to the given line. The line through one end of that diameter, parallel to the given line, is a tangent.
- Any parallel line closer to the centre than the radius (e.g. through the centre) is a secant.
Answer: Construction as described
Done the NCERT exercises? The board paper asks more
Circles has 38 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Circles in our sample papers: Sample paper 1 (questions 9, 23, 28, 29, 33) · Sample paper 2 (questions 10, 31, 33) · Sample paper 3 (questions 11, 29, 33) · Sample paper 4 (questions 10, 11, 19, 30) · Sample paper 5 (questions 11, 12, 29, 33).
Also useful: free MCQs and case studies for Circles · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
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