The points P(a,b) and Q(0,c) are on the curve y/c = cosh (x/c). The line through Q parallel to the normal at P cuts the x-axis at R. Prove that QR = b.
Trivial. [Let O be the origin. Then OR/OQ = sinh a/c, so QR2 = c2(1 + sinh2a/c), so QR = b.]
2nd Putnam 1939
© John Scholes
4 Sep 1999