Chapter 10 · Constructions

NCERT Exemplar Class 10 Maths Exercise 10.3

All 4 questions of NCERT Exemplar Class 10 Maths Exercise 10.3 (Constructions), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Draw a line ​segment of ​length 7 cm. ​Find a point P on ​it which divides it in the ​ratio 3:5.
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   P divides AB in the ratio $3:5$, with $AP=2.625$ cm and $PB=4.375$ cm; constructed via 8 equal divisions on an auxiliary ray.

   Step-by-step solution →
2. Q2
   Draw ​a ​right triangle ABC in which BC = 12 cm, AB = ​5 cm and $\angle B=90^{\circ }$. Construct a triangle similar to ​it and of ​scale ​factor $\frac{2}{3}$. ​Is the new triangle also a right triangle?
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   Construct $△A^{\prime }B{C}^{\prime }$ with $B{C}^{\prime }=8$ cm and $A^{\prime }B=\frac{10}{3}$ cm, similar to $△ABC$ at ratio $2/3$. Yes, it is also a right triangle (right angle at $B$).

   Step-by-step solution →
3. Q3
   Draw ​a ​triangle ABC in which $BC=6$ cm, $CA=5$ ​cm and $AB=4$ ​cm. ​Construct a ​triangle ​similar to it and of scale factor $\frac{5}{3}$.
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   Triangle A'BC' similar to ABC with all sides $\frac{5}{3}$ times longer is obtained by the ray-division construction.

   Step-by-step solution →
4. Q4
   Construct a ​tangent ​to a ​circle ​of radius 4 cm from a point which ​is at a distance of ​6 cm from its centre.
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   Construct the circle on OP as diameter; it meets the given circle at the tangent points T, T'. The tangent length $PT=\sqrt{20}\approx 4.47$ cm.

   Step-by-step solution →