## Chapter 10 Circles Exercise 10.1

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

Answer:There are infinitely many tangents that a circle can have.

Answer:

**Question 2: Fill in the blanks:**

(i) A tangent to a circle intersects it in

(ii) A line intersecting a circle in two points is called a

(iii) A circle can have

(iv) The common point of a tangent to a circle and the circle is called

(i) A tangent to a circle intersects it in

__1__point (s).(ii) A line intersecting a circle in two points is called a

__secant__.(iii) A circle can have

__2__parallel tangents at the most.(iv) The common point of a tangent to a circle and the circle is called

__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) 119 cm

Answer:

a) 12 cm

b) 13 cm

c) 8.5 cm

d) 119 cm

Answer:

Given:

Radius of the circle = 5 cm

OQ = 12 cm

∠ OPQ = 90° (as the tangent to a circle is perpendicular to the radius through the point of contact)

PQ² = OQ² - OP² (by Pythagoras theorem)

= PQ² = (12)² - (5)²

= PQ = √(144 - 25)

= PQ = √199

Hence, the correct option is d) √119.

**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.**

Answer:Here in the above figure, AB is the given line. CD is the tangent to the given circle, which intersects the circle at Q, is parallel to AB. EF is a secant parallel to AB.

Answer:

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