J P Mohindru and Bharat Mohindru Solutions for Chapter: Constructions, Exercise 4: COMPETITION FILE

To divide a line segment $\mathrm{AB}$ in the ratio $5:7$, first a ray $\mathrm{AX}$ is drawn so that $\angle \mathrm{BAX}$ is an acute angle and then at equal distances points are marked on the ray $\mathrm{AX}$ such that the minimum number of these points is

To divide a line segment $AB$ in the ratio $4:7$, a ray $AX$ is drawn first such that $\angle BAX$ is an acute angle and then points $A_1, A_2, A_3, ...$ are located at equal distances on the ray $AX$ and the point $B$ is joined to 

To divide a line segment $\mathrm{AB}$ in the ratio $5:6$, draw a ray $\mathrm{AX}$ such that $\angle \mathrm{BAX}$ is an acute angle, then a ray $\mathrm{BY}$ parallel to $\mathrm{AX}$ and the points ${\mathrm{A}}_1, {\mathrm{A}}_2, {\mathrm{A}}_3, ...$ and ${\mathrm{B}}_1, {\mathrm{B}}_2, {\mathrm{B}}_3, ...$ are located at equal distances on ray $\mathrm{AX}$ and $\mathrm{BY}$ respectively. Then the point joined are:

To construct a triangle similar to a given $△\mathrm{ABC}$ with its sides $\frac{3}{7}$ of the corresponding sides of $△\mathrm{ABC}$, first draw a ray $\mathrm{BX}$ such that $\angle \mathrm{CBX}$ is an acute angle, and $\mathrm{X}$ lies on the opposite side of $\mathrm{A}$ with respect to $\mathrm{BC}$. Then locate points ${\mathrm{B}}_1, {\mathrm{B}}_2, {\mathrm{B}}_3, ...$ on $\mathrm{BX}$ at equal distances and next step is to join

To construct a triangle similar to a given $△\mathrm{ABC}$ with its side $\frac{8}{5}$ of the corresponding sides of $△\mathrm{ABC}$, we draw a ray $\mathrm{BX}$ such that $\angle \mathrm{CBX}$ is an acute angle, and $\mathrm{X}$ is on the opposite side of $\mathrm{A}$ with respect to $\mathrm{BC}$. The minimum number of points to be located at equal distances on ray $\mathrm{BX}$  is

To draw a pair of tangents to a circle which are inclined to each other at an angle of $60°$, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be