CBSE Class 10-Mathematics: Chapter –11 Constructions Part 10
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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.

Let ABC be a Right Triangle
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.

Construct a Triangle of Sides
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

Construct an Isosceles Triangle