MathDB

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

Source:

August 7, 2019

ratiofixedgeometrymidpointsCyclic

Problem Statement

The quadrilateral

ABCD

is inscribed in a fixed circle. It has

AB

parallel to

CD

and the length

AC

is fixed, but it is otherwise allowed to vary. If

h

is the distance between the midpoints of

AC

and

BD

and

k

is the distance between the midpoints of

AB

and

CD

, show that the ratio

h/k

remains constant.