Draw $\overline{\mathrm{XY}}$ of length $7 \mathrm{cm}.$ Find a point $\mathrm{Z}$ on it such that $\mathrm{XZ}=2.5 \mathrm{cm}$Using a ruler and compasses, construct a perpendicular $\overline{\mathrm{XY}}$ through $\mathrm{Z}$.

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?