NCERT Solutions Class 10 Maths
Chapter – 10 (Circles)
The NCERT Solutions in English Language for Class 10 Mathematics Chapter – 10 Circles Exercise 10.1 has been provided here to help the students in solving the questions from this exercise.
Chapter : 10 Circles
Exercise – 10.1
1. How many tangents can a circle have?
Solution – A circle can have infinite tangents.
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 ________
Solution –
(i) A tangent to a circle intersects it in one point(s).
(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 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 – We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent.
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 parallel lines. Line segment AB is the tangent at point C, while line segment XY is the secant.
