Asish Kumar Solutions for Chapter: Geometrical Construction, Exercise 1: Exercise

Draw a line segment of length $\mathrm{AB}=10.6 \mathrm{cm}$. Construct its perpendicular bisector.

Draw a line segment of length $7.4 \mathrm{cm}$. Draw a perpendicular bisector to the line from point $\mathrm{O}$ lying outside the line segment.

Compare the line segments by measurement.

Draw a circle with radius 6 cm and centre at point O. Mark a point on the circle.

Draw a circle with radius $6 \mathrm{cm}$ and centre at point $\mathrm{O}$. Mark a point inside the circle.

Draw a circle with radius $6 \mathrm{cm}$ and centre at point $\mathrm{O}$. Mark a point outside the circle.

Draw a line segment $\mathrm{PQ}=8 \mathrm{cm}$. Draw its perpendicular bisector which will give the mid-point of $\mathrm{PQ}$. Mark it as $\mathrm{O}$. With $\mathrm{O}$ as centre and $\mathrm{OP}$ or $\mathrm{OQ}$ as radius, draw a circle. The circle cuts the perpendicular bisector at points $\mathrm{R}$ and $\mathrm{S}$. What is the line $\mathrm{ROS}$ with respect to the circle?

Draw a circle with centre $\mathrm{O}$ and radius $5 \mathrm{cm}$. Mark $\mathrm{X}$ — a point on the circumference. Take $\mathrm{X}$ as centre and draw another circle with radius $5 \mathrm{cm}$. Does the circle now drawn pass through point $\mathrm{O}$? Explain with reasons.