10th Maths 10.1

NCERT Class 10th solution of Exercise 10.2

NCERT Class 10th Maths Projects

Exercise 10.1

Q1. How many tangents can a circle have?

Answer:

Infinitely many.

Q2. Fill in the blanks:

i) A tangents 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 ______.

Answer:

i) `1`    ii) secant    iii) `2`    iv) point of contact.

Q3. 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) `sqrt119 cm`

Answer:

D) `sqrt119 cm`

Q4. 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.

Sol. :

Step of Construction:-

1) Draw a circle of centre `O` and any radius.

2) Draw `OR ⊥ EF,` which intersects the circle at point `Q.`

3) Draw `CD ⊥ OR` through point `Q` of the circle.

4) Through any point `P` on the `OR` inside the circle draw another line `AB ⊥ OR` which intersects the circle at point `G` and `H`.

Thus the line `AB`is a required secant and `CD` is the required tangent to the circle both parallel to the given line `EF`.