Question 25
a. Let $\mathcal{C}$ be a circle with center $O$ and radius $r$ and $X$ an outside point to $\mathcal{C}$. We built a center circumference at $X$ passing through $O$, which intersects $\mathcal{C}$ at points $P$ and $Q$. With center in $P$ we built a circle passing through $O$ and with center in $Q$ we built another circle passing through $O$. These two circles intersect at points $O$ and $Y$. Prove that $OX \times OY = r^2$.
b. is given a segment $AB$. Show how to build, using only compass, a point $C$ such that $B$ is the midpoint of the segment $AC$.
c. is given a segment $AB$. Show how to build, using only compass, the midpoint of the segment $AB$.
b. is given a segment $AB$. Show how to build, using only compass, a point $C$ such that $B$ is the midpoint of the segment $AC$.
c. is given a segment $AB$. Show how to build, using only compass, the midpoint of the segment $AB$.