5

Part of 1999 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

max of sum of distances of point of semicircle from 3 sides of cyclic ABCD

Source: Rioplatense level 3 p5

The quadrilateral

ABCD

is inscribed in a circle of radius

1

AB

is a diameter of the circumference and

CD = 1

. A variable point

X

moves along the semicircle determined by

AB

that does not contain

C

D

. Determine the position of

X

for which the sum of the distances from

X

BC, CD

DA

geometrydistancemaximumsemicirclecyclic quadrilateral