HBSE 10th Class Maths Solutions Chapter 10 Circles Ex 10.1

Haryana State Board HBSE 10th Class Maths Solutions Chapter 10 Circles Ex 10.1 Textbook Exercise Questions and Answers.

Haryana Board 10th Class Maths Solutions Chapter 10 Circles Ex 10.1

Question 1.
How many tangents can a circle have?
Solution :
A circle can have infinitely many tangents.

Question 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 ……………….
Answers :
(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
Solution :
Let O be the centre of the circle.
Let P be a point on circle such that OP = 5cm.
Now, PQ is a tangent at P and OP is a radius through P.
Since, the tangent at a point on a circle is perpendicular to the radius through the point of contact.
∴ OP ⊥ PQ.
In right ∆OPQ, we have
OQ² = OP² + PQ² [By Pythagoras theorem]

⇒ PQ² = 119
⇒ PQ = \(\sqrt{119}\) cm
Hence, Length of PQ = \(\sqrt{119}\) cm.
So, correct option is (D).

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.

Solution :
In figure line m is parallel to line n and also tangent to the given circle at the point P.
Another line l is parallel to the given line n and also a secant to the circle.