# CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## 4 Mark Questions

**Question 1**:

Construct a in which and . Also construct a triangle ABC similar to whose each side is times the corresponding side of the .

**Answer**:

Steps of construction: 1. Draw a line segment . 2. At B construct .

3. With B as center and radius draw an arc intersecting BX at C. 4. Join AC. Triangle so obtained is the required triangle. 5. Construct an acute angle at A on opposite side of vertex C of

6. Locate 3 points on AY such that .

7. Join to B and draw the line through parallel to intersecting the extended line segment AB at B ′ .

8. Draw a line through B ‘parallel to BC intersecting the extended line seg. AC at C’ . 9. so obtained is the required triangle

**Question 2**:

Draw a circle of radius from a point P, from the centre of the circle, draw a pair of tangents to the circle measure the length of each tangent segment.

**Answer**:

Steps of construction:

1. Take a point O in the plane of a paper and draw a circle of the radius . 2. Make a point P at a distance of from the centre O and Join OP. 3. Bisect the line segment OP. Let be the mid-point of OP. 4. Taking M as a centre and OM as radius draw a circle to intersect the given circle at the points T and T. ′ 5. Join PT and PT, ′ then PT and PT ′ are required tangents.

**Question 3**:

Draw a right triangle in which the sides containing the right angle are and . Construct a similar triangle whose sides are times the sides of the above triangle.

**Answer**:

Steps of construction:

1. Draw a line segment .

2. At B construct .

3. With B as center and radius draw an arc intersecting the ray BX at A.

4. Join AC to obtain the required

5. Draw any ray BY making an acute angle with BC on the opposite side to the vertex A.

6. Locate 5 points on by so that .

7. Join to C and draw a line through parallel to intersecting the extended line segment BC at C ′ .

8. Draw a line through C ‘parallel to CA intersecting the extended line segment BA at A’ .

Thus, DA ‘BC’ is the required right triangle.

**Question 4**:

Construct a circle whose radius is equal to . Let P be a point whose distance from its centre is . Construct two tangents to it from P.

**Answer**:

Steps of construction:

1. Take a point O in the plane of the paper and draw a circle of radius 4cm.

2. Make a point P at a distance of 6cm from the center O and join OP.

3. Bisect the line segment OP. Let the point of bisection be M.

4. Taking M as center and OM as radius, draw a circle to intersect the given circle at the point T and T ′ .

5. Join PT and PT ′ to get the required tangents