Question

Let $\mathrm{P}$ and $\mathrm{Q}$ be the center of two circles of equal radii, draw them so that each one of them passes through the center of the other. let them intersect at $\mathrm{M}$ and $\mathrm{N}$ examine whether $\overline{PQ}\perp \overline{MN}$

Answer 1

1. Draw the circle of radius $5$ cm (assume radius = $5$ cm).
2. Mark the center as$\mathrm{P}$.

3) From the outer boundary of the circle (any point on the circumference) make another circle without changing the compass dimension

4) Mark the new center as $\mathrm{Q}$ which will produce the line segment $\overline{PQ}$

5) Let the intersection of two circles as $\mathrm{M}$ and $\mathrm{N}$ respectively, Join $\mathrm{M}$ and $\mathrm{N}$ use ruler which will produce the line segment $\overline{MN}$

6) Hence the line segment $\overline{PQ}\perp \overline{MN}$