MathDB

AL _|_ BC wanted, altitudes, projections

Source: 7th QEDMO problem 12 (14. - 17. 1. 2010) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 9, 2021

perpendiculargeometry

Problem Statement

Let

Y

and

Z

be the feet of the altitudes of a triangle

ABC

drawn from angles

B

and

C

, respectively. Let

U

and

V

be the feet of the perpendiculars from

Y

and

Z

on the straight line

BC

. The straight lines

YV

and

ZU

intersect at a point

L

. Prove that

AL \perp BC