Question 53
A parallelogram $ABCD$ has side lengths $|AB|=7\,\mathrm{cm}$ and $|BC|=5\,\mathrm{cm}$. Its altitude to $AB$ is $4\,\mathrm{cm}$, and $\alpha=\angle BAD$ is acute.
Part a. Construct the parallelogram with straightedge and compass, and draw the circumcircle of triangle $BCD$. Label the circumcenter $S$.
Part b. Round the larger of the two angles $\angle BSD$ (the reflex angle) to $254^\circ$ and use this value in subsequent calculations. Find the interior angles of the parallelogram.
Part c. Find the obtuse angle between the perpendicular bisector of $AD$ and the altitude to $AB$.
Part a. Construct the parallelogram with straightedge and compass, and draw the circumcircle of triangle $BCD$. Label the circumcenter $S$.
Part b. Round the larger of the two angles $\angle BSD$ (the reflex angle) to $254^\circ$ and use this value in subsequent calculations. Find the interior angles of the parallelogram.
Part c. Find the obtuse angle between the perpendicular bisector of $AD$ and the altitude to $AB$.