standard_description: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
problem_activity: Task
Let $C$ be a circle with center $O$ and a diameter meeting $C$ in points
$P$ and $S$ as shown below:
[IMG]
With straightedge and compass, show how to find  a point $Q$ on $C$ so that triangle $OPQ$ is equilateral.
Repeating part (a) show how to find points $R, T, U$ on $C$ so that
$PQRSTU$ is a regular hexagon.
Find the area of $PQRSTU$.  How does it compare to the area of $C$?


aligns: no