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trapezoid, 4 perpendiculars, collinear ? (2017 HOMC Junior Q14)

Source:

August 3, 2019

geometrytrapezoidcollinearcollinearityperpendicular

Problem Statement

Given trapezoid

ABCD

with bases

AB \parallel CD

(

AB < CD

). Let

O

be the intersection of

AC

and

BD

. Two straight lines from

D

and

C

are perpendicular to

AC

and

BD

intersect at

E

, i.e.

CE \perp BD

and

DE \perp AC

. By analogy,

AF \perp BD

and

BF \perp AC

. Are three points

E , O, F

located on the same line?

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