# CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## 1 Mark Questions

**Question 1**:

The length of tangent from a point A at a distance of 5 cm from the center of the circle is 4 cm. What will be the radius of circle?

(a)

(b)

(c)

(d) None of these

**Answer**:

(c)

**Question 2**:

In the figure given below, PA and PB are tangents to the circle drawn from an external point . is a third tangent touching the circle at Q. If and , what is the length of ?

(a)

(b)

(c)

(d)

**Answer**:

(a)

**Question 3**:

The tangent of a circle makes angle with radius at point of contact

(a)

(b)

(c)

(d) None of these

**Answer**:

(c)

**Question 4**:

If tangent PA and PB from a point P to a circle with center are inclined to each other at an angle of , then what is the value of ?

(a)

(b)

(c)

(d)

**Answer**:

(b)

## 2 Mark Questions

**Question 1**:

In each of the following, give the justification of the construction also:

Draw a circle of radius . From a point away from its centre, construct the pair of tangents to the circle and measure their lengths.

**Answer**:

Given: A circle whose center is O and radius is 6 cm and a point P is 10 cm away from its center. To construct: To construct the pair of tangents to the circle and measure their lengths.

Steps of Construction:

(a) Join and bisect it. Let be the mid-point of .

(b) Taking M as center and as radius, draw a circle. Let it intersects the given circle at the points Q and R.

(c) Join PQ and PR. Then PQ and PR are the required two tangents. By measurement,

Justification: Join and . Since and are the angles in semicircles.

Also, since OQ, OR are radii of the circle, PQ and PR will be the tangents to the circle at Q and R, respectively. We may see that the circle with OP as diameter increases the given circle in two points. Therefore, only two tangents can be draw.