IMO 1968 SL 10

Consider two segments of length … (…) and a segment of length ….

imoshortlistmathematicsolympiad

IMO 1968 SL 10

Origin: ROM

Problem

Consider two segments of length $a, b$ ($a > b$) and a segment of length $c = \sqrt{ab}$.

(a) For what values of $a/b$ can these segments be sides of a triangle?

(b) For what values of $a/b$ is this triangle right-angled, obtuse-angled, or acute-angled?