NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 10: Construction

Exercise 10.2

By geometrical construction, it is possible to divide a line segment in the ratio \(\sqrt{3} : \dfrac{1}{\sqrt{3}}\).

To construct a triangle similar to a given \(\triangle ABC\) with its sides \(\dfrac{7}{3}\) of the corresponding sides of \(\triangle ABC\), draw a ray \(BX\) making an acute angle with \(BC\) and with \(X\) on the opposite side of \(A\) w.r.t. \(BC\). Locate points \(B_1,B_2,\dots,B_7\) at equal distances on \(BX\). Then join \(B_3\) to \(C\) and draw \(B_6C'\) \(\parallel\) \(B_3C\) meeting \(BC\) produced at \(C'\). Finally, draw \(A'C'\) \(\parallel\) \(AC\).

A pair of tangents can be constructed from a point \(P\) to a circle of radius \(3.5\,\text{cm}\) situated at a distance of \(3\,\text{cm}\) from the centre.

A pair of tangents can be constructed to a circle inclined at an angle of \(170^\circ\).