Difference between revisions of "2008 UNCO Math Contest II Problems/Problem 4"
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== Problem == | == Problem == | ||
+ | In the figure there are <math>8</math> line segments drawn from | ||
+ | vertex <math>A</math> to the base <math>BC</math> (not counting the segments <math>AB</math> or <math>AC</math>). | ||
− | + | <asy> | |
− | + | for (int x=0;x<11;++x){ | |
+ | draw((5,15)--(x,0),dot); | ||
+ | } | ||
+ | draw((0,0)--(10,0),black); | ||
+ | draw((10/6,5)--(10-10/6,5),black); | ||
+ | draw((20/6,10)--(10-20/6,10),black); | ||
+ | MP("A",(5,15),N);MP("B",(0,0),W);MP("C",(10,0),E); | ||
+ | </asy> | ||
− | (a) Determine the | + | (a) Determine the total number of triangles of all sizes. |
− | (b) | + | (b) How many triangles are there if there are <math>n</math> lines |
+ | drawn from <math>A</math> to <math>n</math> interior points on <math>BC</math>? | ||
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{{UNCO Math Contest box|n=II|year=2008|num-b=3|num-a=5}} | {{UNCO Math Contest box|n=II|year=2008|num-b=3|num-a=5}} | ||
− | [[Category:Intermediate | + | [[Category:Intermediate Geometry Problems]] |
Revision as of 22:55, 19 October 2014
Problem
In the figure there are line segments drawn from
vertex
to the base
(not counting the segments
or
).
(a) Determine the total number of triangles of all sizes.
(b) How many triangles are there if there are lines
drawn from
to
interior points on
?
Solution
See Also
2008 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |