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

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**Question 16**:

Draw a with side , and , then construct a triangle whose sides are times the corresponding sides of .

**Answer**:

Steps of construction:

1. Draw in which , and .

2. Locate 4 points and on BZ such that .

3. Join and draw .

4. Now Draw .

5. is the required triangle.

**Question 17**:

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. Draw a circle with center O and radius .

2. Mark point P at a distance of from the centre O and join OP.

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

4. Take M as center and OM as radius draw a circle to intersect the given circle at the points T and T ′ .

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

**Question 18**:

Draw a line segment AB of length taking A as centre, draw a circle of radius and taking B as centre, draw another circle of radius . Construct tangents to each circle from the centre to the other circle.

**Answer**:

Steps of construction:

1. Draw a line segment .

2. Taking A as center and radius draw a circle.

3. Taking B as center and radius draw another circle.

4. Bisect the line segment AB, let the point of bisection be M.

5. Taking M as center and MA as radius, draw a circle intersecting the given circles at the point .

**Question 19**:

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 in which , and .

2. Draw acute .

3. Locate 3 points on BX so that

4. Join and draw .

5. Now Draw .

Thus, is the required triangle.