NCERT Solutions
Class 10 - Mathematics - Chapter 10: CIRCLES
Exercise 10.1

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Question. 1

How many tangents can a circle have?

Answer:

Infinitely many

Question. 2

Fill in the blanks:

  1. A tangent to a circle intersects it in ______ point(s).
  2. A line intersecting a circle in two points is called a ______.
  3. A circle can have ______ parallel tangents at the most.
  4. The common point of a tangent to a circle and the circle is called ______.

Answer:

(i) One

(ii) Secant

(iii) Two

(iv) Point of contact

Question. 3

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is:

(A) 12 cm    (B) 13 cm    (C) 8.5 cm    (D) \(\sqrt{119}\) cm

Answer:

Option D, \(\sqrt{119}\text{ cm}\)

Question. 4

Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.