# CBSE Class 10-Mathematics: Chapter – 11 Constructions Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 5**:

Draw a triangle ABC with sides , and . Then construct a triangle whose sides are times the corresponding sides of

**Answer**:

Steps of construction:

1. Draw a line segment .

2. At B make .

3. With B as center and radius equal to , draw an arc intersecting BX at A.

4. Join AC, then DABC is the required triangle.

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

6. Locate the 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 triangle.

**Question 6**:

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 .

2. Draw any diameter .

3. Construct meeting the circle at B.

4. At A and B draw perpendiculars to OA and OB intersecting at P.

5. PA and PB are required tangents and .

**Question 7**:

Draw the tangents at the extremities of a diameter AB of a circle of radius . Are these tangents parallel? Given reasons.

**Answer**:

Steps of construction:

1. Draw a circle of radius .

2. Draw any diameter .

3. Draw

4. AT and BM are tangents extremities of the diameter AB.

5.

, they are alternate angles.

**Question 8**:

Construct a in which , and . Now construct a triangle similar to such that each of its sides is two-third of the corresponding sides of . Also prove your assertion.

**Answer**:

Steps of construction:

1. Draw with sides , and .

2. Below BC make acute .

3. Along BX mark off three points such that .

4. Join .

5. Draw and

Thus, is the required triangle