MathDB

NK // ML wanted, trapezoid and 2 circles with diameters legs related

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 3.6 day2

September 30, 2021

geometrytrapezoidparallel

Problem Statement

Given the trapezoid

ABCD

with the

BC\parallel AD

, let

C_1

and

C_2

be circles with diameters

AB

and

CD

respectively. Let

M

and

N

be the intersection points of

C_1

with

AC

and

BD

respectively. Let

K

and

L

be the intersection points of

C_2

with

AC

and

BD

respectively. Given

M\ne A

N\ne B

K\ne C

L\ne D

. Prove that

NK \parallel ML