Monday, August 17, 2009

KBB2 Problem 8

We are given a circle centered on $O$ with radius $r$, and given lengths $a,b$ with $a > b$. We are also given a point $P$ on the circle.

For any point $B$ on the circle, construct a point $A$ such that $AP = a, BP = b$. Also construct rhombus $ABCD$ such that $D,B,P$ lie on the same line.

Suppose $B$ moves around the circle and we repeat the construction process above, as long as there is a point $A$ that satisfies the conditions. Show that as $B$ moves around the circle, the resulting point $D$ will trace a straight line. Determine the angle formed by that line and $PO$.