NCERT Solutions for Class 10 Maths Chapter 10 – Circles
1. How many tangents can a circle have?
2. Fill in the blanks:
(i) A tangent to a circle intersects it in _______________ point(s).
(ii) A line intersecting a circle in two points is called a _______________.
(iii) A circle can have _______________ parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called _________.
(ii) A line intersecting a circle in two points is called a secant.
(iii) A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called point of contact.
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) cm
OPQ = [The tangent at any point of a circle is to the radius through the point of contact]
In right triangle OPQ,
OQ2 = OP2 + PQ2 [By Pythagoras theorem]
= 144 – 25 = 119
PQ = cm
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.