# CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 9**:

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

**Answer**:

Steps of construction:

1. Construct a is which and .

2. Draw a ray AX making any acute angle with AB on the opposite side of the vertex C.

3. Cut three equal parts from AX say

.

4. Join to B.

5. From draw at

6. At B ′ draw intersecting at .

7. is required triangle similar to .

**Question 10**:

Draw a pair of tangents to a circle of radius which are inclined to each other at

**Answer**:

Steps of construction:

1. Draw a circle with center O and radius 5cm.

2. Draw any radius OT.

3. Construct

4. Draw and . Then and PT are the two required tangents such that

. Here,

**Question 11**:

Draw a circle of radius with centre O. Draw a diameter POQ. Through P or Q draw tangent to the circle.

**Answer**:

Steps of construction:

1. Draw a circle of radius 4 cm.

2. Draw diameter .

3. Construct .

4. Produce PQ to , then is the required tangent at the point Q.

**Question 12**:

Construct a triangle with sides , and and then another triangle whose sides are of the corresponding sides of first triangle.

**Answer**:

Steps of construction:

1. Draw a line segment .

2. With A as center and radius draw an arc.

3. Again B as center and radius draw another arc cutting the previous arc at C. Join AC and BC, then DABC is required triangle.

4. Draw any ray AX making acute angle.

5. Locate points on AX so that

6. Join to B and draw a line through parallel to intersecting the extended line segment AB at .

7. Draw , then is the required triangle