Problem #91

Consider a point in the plane that has two perpendicular lines through it that pass through two given points. In the figure below, A and B are the given points and P and Q are points such that angle APB and angle AQB are right angles. It is well-known that the set of all such points is a circle with the segment between the two given points as diameter.

Consider a point in space that has three mutually perpendicular lines through it that each pass through the circle x2 + y2 = 1 in the xy-plane. In the figure below, A, B, and C are points on the circle and angles APB, APC, and BPC are all right angles. Find the locus of all such points P.


Back to the Advanced Problem Archives

Back to the Math Department Homepage.