Construct a circle of radius $4 \mathrm{cm}$. Name the centre as $\mathrm{O}$. Now draw a chord $\mathrm{AB}$ and construct a perpendicular from $\mathrm{O}$ on the chord $\mathrm{AB}$. Name the point where the perpendicular intersects the chord $\mathrm{AB}$ as $\mathrm{M}$. Measure the lengths of $\overline{\mathrm{AM}}$ and $\overline{\mathrm{MB}}$. What do you conclude?

Draw an angle measure $40˚$ by using a protractor. Now using compass and a ruler and construct an angle equal to the given angle.

Draw an angle measure $40˚$ by using a protractor. Now using compasses and a ruler only, construct an angle of twice the measure of the given angle.

Draw an angle of measure $40˚$ by using a protractor. Now using compasses and a ruler only, construct an angle of half the measure of the given angle.