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.