# NCERT Solutions for Class 10 Maths Exercise 11.2

NCERT Solutions for Class 10 Maths Exercise 11.2 Constructions. Ex. 11.2 explains how to draw tangents to a given circle under different situations. Videos are given here related to exercise 11.2

2 so that students of different board like CBSE, UP Board, MP Board, Gujrat Board, etc., can understand easily without any further guidance. PDF solutions are also available for ex. 11.2 of class 10, so that students can use it offline. Study online or offline, its depends but the regular practice is required to perform better in exams.

## Class 10 Maths Exercise 11.2 Solution in Hindi and English Medium

 Class: 10 Mathematics Chapter: 11 Constructions Exercise: 11.2 NCERT Solutions in PDF and Videos

### Class 10 Maths Exercise 11.2 Solution in Video

#### Construction of Tangents to a Circle

We have already studied in Chapter 10 of Chapter 10 that if a point is inside a circle, there cannot be a tangent to the circle through this point. However, if a point is on a circle, the circle at this point has only one tangent and is perpendicular to the radius passing through this point. So if we want to draw a tangent to a point on a circle, simply draw a radius through this point and draw a line perpendicular to this radius through this point and it will be the tangent required to the point. We have also seen that if the point is outside the circle, the circle will have two tangents from this point. In this section, we will learn how to construct a tangent from a point outside it to a circle.

##### Tangent to a Circle

We are given a circle with center O and a point P outside it. We have to construct two tangent lines of P.
construction phase:

1. Join PO and Bisect. M is the midpoint of PO.
2. Draw a circle, taking M as the center and MO as the radius. Divide the given circle at the points Q and R.
3. Join PQ and PR. Then PQ and PR are the two tangents, which we are trying to make. Now we will learn how this complete construction works. Join OQ. Then ic PQO is an angle in the semicircle and hence O PQO = 90 °
4. Now, we can say that PQ, OQ.
5. Since OQ is a radius of a given circle, PQ must be tangent to the circle. Similarly, PR is also a tangent to the circle.

###### Centre of Circle is required

If the center of the circle is not given, you can locate its center by first taking two non-parallel cords and then finding the point of intersection of their perpendicular bisector. You can then proceed to draw the tangent in the given circle.

##### How many tangents can we draw from a point outside of a circle?

Only two tangents can be drawn from a point given outside the circle.

##### If point is on the circle, then what will be the maximum number of tangent to circle from this point?

In this case, we can draw only one tangent.

##### Which question is most important from Exercise 11.2 of class 10 Maths?

Question 3 and Question 7 are the questions which are frequently asked in the CBSE board examination.

##### Which is the most frequent question asked in CBSE Board Exams?

Question 7 (sometime as it is but most of the time modified format) is the frequently asked question in board exams.          