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Ratio in acute triangle with lines through feet of altitudes

Source: XIX Olimpíada Matemática Rioplatense (2010)

July 22, 2011

ratiogeometry unsolvedgeometry

Problem Statement

Acute triangle

ABP

, where

AB > BP

, has altitudes

BH

PQ

, and

AS

. Let

C

denote the intersection of lines

QS

and

AP

, and let

L

denote the intersection of lines

HS

and

BC

. If

HS = SL

and

HL

is perpendicular to

BC

, find the value of

\frac{SL}{SC}