High School Geometry
Several hours later and after taking several routes to this problem I'm stumped>>>PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles?

Thank you, Chris

Chris,

Draw an accurate picture, and draw the circle through P,Q and X. Note that it will go through Y. Guess where its center is.