MathDB

467

Part of 1988 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 467 All Soviet Union MO 1988 fixed ratio of distances of midpoints

Source:

8/7/2019
The quadrilateral ABCDABCD is inscribed in a fixed circle. It has ABAB parallel to CDCD and the length ACAC is fixed, but it is otherwise allowed to vary. If hh is the distance between the midpoints of ACAC and BDBD and kk is the distance between the midpoints of ABAB and CDCD, show that the ratio h/kh/k remains constant.
ratiofixedgeometrymidpointsCyclic