## Chapter 10 Circles Ex 10.1

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

There can be infinitely many tangents to a circle.

**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 ……….. . **Solution:** **(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)** 199−−−√ cm **Solution:**

Radius of the circle = 5 cm

OQ = 12 cm

∠OPQ = 90°

[The tangent to a circle is perpendicular to the radius through the point of contact]

PQ^{2} = OQ^{2} – OP^{2} [By Pythagoras theorem]

PQ^{2} = 12^{2} – 5^{2} = 144 – 25 = 199

PQ = 199−−−√ cm.

Hence 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:**

A line m is parallel to the line n and a line l which is secant is parallel to the given line.