** Maths Class 10 Exercise 10.1**

**1.
How many tangents can a circle have?**

**Answer:** Since
there are infinitely many points on the circumference of a circle and at each
point we can draw a unique tangent, therefore, a circle can have infinitely
many tangents.

**2.
Fill in the blanks:**

**(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 __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: (D) **Since, PQ is
the tangent and OP is the radius through the point of contact.

Therefore, ∠OPQ = 90°

[Since, the tangent at any point of a circle
is perpendicular to
the radius through the point of contact.]

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

(12)^{2 }= (5)^{2 }+ (PQ)^{2}

144 = 25 + PQ^{2}

PQ^{2 }= 144 – 25 = 119

PQ = √119 cm

**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:
**