NCERT Solution Class 10 Maths Chapter – 10 Circles Exercise – 10.1

1. How many tangents can a circle have?

Solution: There can be infinite tangents to a circle. A circle is made up of infinite points which are at an equal distance from a point. Since there are infinite points on the circumference of a circle, infinite tangents can be drawn from them.

2. Fill in the blanks:

(i) A tangent to a circle intersects it in …………… point(s).
Solution: A tangent to a circle intersects it in one point(s).

(ii) A line intersecting a circle in two points is called a ………….
Solution: A line intersecting a circle in two points is called a secant.

(iii) A circle can have …………… parallel tangents at the most.
Solution: 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 …………
Solution: The common point of a tangent to a circle and the circle is called the 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) √119 cm

Solution:

In the above figure, the line that is drawn from the centre of the given circle to the tangent PQ is perpendicular to PQ.
And so, OP ⊥ PQ
Using Pythagoras theorem in triangle ΔOPQ we get,
OQ² = OP²+PQ²
(12)² = 5²+PQ²
PQ² = 144 – 25
PQ² = 119
PQ = √119 cm
So, option D i.e. √119 cm is the length of PQ.

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.

Solution:

In the above figure, XY and AB are two the parallel lines. The line segment AB is the tangent at point C while the line segment XY is the secant.