Difference between revisions of "1970 Canadian MO Problems/Problem 2"
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+ | <asy> | ||
+ | draw((0,0)--(5,0)--(16/5,12/5)--cycle,dot); | ||
+ | draw((2.5,0)--(2.5,7.5/4)--(5,0)--cycle,black); | ||
+ | MP("C",(0,0),SW);MP("D",(16/5,12/5),N);MP("B",(5,0),SE); | ||
+ | MP("E",(2.5,0),NE);MP("A",(2.5,7.5/4),N); | ||
+ | MP("h",(2.5,7.5/8),W);MP("k",(41/10,6/5),NE); | ||
+ | draw((-.2,.2)--(2.5-.2,7.5/4+.2),arrow=ArcArrow(TeXHead)); | ||
+ | draw((2.5-.2,7.5/4+.2)--(-.2,.2),arrow=ArcArrow(TeXHead)); | ||
+ | MP("b",(2.3/2-.05,7.5/8+.25),N); | ||
+ | draw((0,-.2)--(5,-.2),arrow=ArcArrow(TeXHead)); | ||
+ | draw((5,-.2)--(0,-.2),arrow=ArcArrow(TeXHead)); | ||
+ | MP("a",(2.5,-.2),S); | ||
+ | draw((16/5,12/5)--(16/5-.2,12/5-.15)--(16/5-.2+.15,12/5-.15-.2)--(16/5+.15,12/5-.2)--cycle,black); | ||
+ | </asy> | ||
+ | |||
+ | |||
+ | == Solution == | ||
== Solution == | == Solution == |
Revision as of 04:32, 8 October 2014
Problem
Given a triangle with angle
obtuse and with altitudes of length
and
as shown in the diagram, prove that
. Find under what conditions
.