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

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**Question 13**:

Let ABC be a right triangle in which , and . BD is the perpendicular from B on AC. The circle through B, C and D is drawn construct the tangents from A to this circle.

**Answer**:

Steps of construction:

1. Draw with , and .

2. Draw perpendicular BD from B to AC.

3. Let O be the mid-point of BC. Draw a circle with centre O and radius . This circle will pass through the point D.

4. Join AO and bisect AO.

5. Draw a circle with centre and as radius cuts the previous circle at B and P.

6. Join AP, AP and AB are required tangents drawn from A to the circle passing through B, C and D.

**Question 14**:

Construct a triangle of sides , and and then a triangle similar to it whose sides are of the corresponding sides of the first triangle

**Answer**:

Steps of construction:

1. Draw with , and .

2. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A. 3. Locate 3 points and on BX so that .

4. Join and draw .

5. Draw a line through such that . Then is the required triangle.

**Question 15**:

Construct an isosceles triangle whose base is 8cm and altitude 4cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.

**Answer**:

Steps of construction:

1. Draw line segment .

2. Draw perpendicular bisector of AB which intersects AB at D.

3. Cut . Join AC and BC. Thus, is the required triangle.

4. Draw acute angle .

5. Locate 3 points on AX so that .

6. Join and draw

7. Draw

8. is the required triangle