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Secant less than half trapezoid perimeter

Source: Iranian Geometry Olympiad 2016 Medium 1

May 26, 2017

geometrytrapezoidperimeter

Problem Statement

In trapezoid

ABCD

with

AB || CD

,

\omega_1

and

\omega_2

are two circles with diameters

AD

and

BC

, respectively. Let

X

and

Y

be two arbitrary points on

\omega_1

and

\omega_2

, respectively. Show that the length of segment

XY

is not more than half the perimeter of

ABCD

.
Proposed by Mahdi Etesami Fard

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