Chapter 10 · Constructions

NCERT Exemplar Class 10 Maths Exercise 10.2

All 4 questions of NCERT Exemplar Class 10 Maths Exercise 10.2 (Constructions), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   By geometrical construction, it ​is possible to divide a line ​segment in the ratio $\sqrt{3}:\frac{1}{\sqrt{3}}$. ​State whether ​this statement ​is ​true or ​false and justify.
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   True

   Step-by-step solution →
2. Q2
   To construct a triangle similar to a given $△ABC$ with its sides $\frac{7}{3}$ ​of the corresponding ​sides of $△ABC$, ​draw ​a ray $BX$ making acute angle with $BC$ and $X$ lies on the ​opposite side of $A$ with respect to $BC$. The points $B_1,B_2,\dots ,B_7$ ​are located at equal distances on $BX$, $B_3$ is joined to $C$ and then a line segment $B_6{C}^{\prime }$ is drawn parallel to $B_{3}C$ where $C^{\prime }$ lies on $BC$ produced. Finally, line segment $A^{\prime }{C}^{\prime }$ is drawn parallel to $CA$. Is ​this construction correct? Justify.
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   No, the construction is incorrect. Drawing the parallel through $B_6$ gives a scale factor $\frac{6}{3}=2$; for $\frac{7}{3}$ the parallel must pass through $B_7$.

   Step-by-step solution →
3. Q3
   Write ​'True' or 'False' and justify your answer: A pair ​of tangents ​can ​be constructed from ​a point ​P to ​a circle of ​radius 3.5 cm situated at a distance of 3 cm from the centre.
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   False. Since the distance $3$ cm is less than the radius $3.5$ cm, $P$ lies inside the circle and no tangent can be drawn.

   Step-by-step solution →
4. Q4
   State whether ​the following ​is ​true or ​false and justify: A pair ​of tangents can be constructed ​to a circle inclined at an angle of $170^{\circ }$.
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   True

   Step-by-step solution →