Construct $\triangle PQR$ where $QR = 5 \; cm$, $\angle Q =45^\circ$ and $PQ = 6.5 \; cm$.
Find by construction points $X$ and $Y$ which are equidistant from $Q$ and $R$, and are $4 \; cm$ from $Q$.
$\triangle PQR$ is constructed with $QR = 5 \; cm$, $\angle Q =45^\circ$ and $PQ = 6.5 \; cm$.
Locus $\left(L_1\right)$ of points which are equidistant from $Q$ and $R$ lie on the perpendicular bisector $AB$ of $QR$.
Locus $\left(L_2\right)$ of points which are at a distance of $4 \; cm$ from $Q$ lie on the circle $C$ with center at $Q$ and radius $4 \; cm$.
Points $X$ and $Y$ lie at the intersection of $L_1$ and $L_2$.