921Crux 2822, proposed by Peter Woo, Biola University, La Mirada,
CA
Suppose thatΠis a parallelogram with sides of lengths 2 aand 2 band
with acute angleα, and thatFandF′are the foci of the ellipseΛthat is
tangent to the four sides ofΠat their midpoints.
(a) Find the major and minor semi-axes ofΠin terms ofa,bandα.
(b) Find a straight-edge and compass construction forFandF′.