Use ruler and compass for this question.
Construct a circle of radius $4.5\mathrm{cm}$.
Draw a chord. $\mathit{A}\mathit{B}=6\mathrm{cm}$.
(i) Find the locus of points equidistant from $\mathit{A}$ and $\mathit{B}$.
Mark the point where it meets the circle as $\mathit{D}$.
(ii) Join $\mathit{A}\mathit{D}$ and find the locus of points which are equidistant from $\mathit{A}\mathit{D}$ and $\mathit{A}\mathit{B}$. Mark the point where it meets the circle as $\mathit{C}$.
(iii) Join $\mathit{B}\mathit{C}$ and $\mathit{C}\mathit{D}$. Measure and write down the length of side $\mathit{C}\mathit{D}$ of the quadrilateral $\mathit{A}\mathit{B}\mathit{C}\mathit{D}$.