MathDB

Concurrence, Isogonality

Source: BMO 2019, Problem 3

May 2, 2019

geometryBMO

Problem Statement

Let

ABC

be an acute scalene triangle. Let

X

and

Y

be two distinct interior points of the segment

BC

such that

AX

. Suppose that:

1)

K

and

S

are the feet of the perpendiculars from from

B

to the lines

AX

and

AY

respectively.

2)

BC

and

L

are the feet of the perpendiculars from

C

to the lines

AX

and

AY

respectively. Prove that

KL

and

ST

intersect on the line

BC

.

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