MathDB

Prove that XY passes through H

Source: Baltic Way 2005

December 28, 2010

geometryrectanglegeometry proposed

Problem Statement

Let the lines

e

and

f

be perpendicular and intersect each other at

H

. Let

A

and

B

lie on

e

and

C

and

D

lie on

f

, such that all five points

A,B,C,D

and

H

are distinct. Let the lines

b

and

d

pass through

B

and

D

respectively, perpendicularly to

AC

; let the lines

a

and

c

pass through

A

and

C

respectively, perpendicularly to

BD

. Let

a

and

b

intersect at

X

and

c

and

d

intersect at

Y

. Prove that

XY

passes through

H

.

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