Difference between revisions of "2008 UNCO Math Contest II Problems/Problem 4"
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== Solution == | == Solution == | ||
| − | + | (a) <math>3\binom{10}{2}</math> (b) <math>3\binom{n+2}{2}=\frac{3(n+1)(n+2)}{2}</math> | |
== See Also == | == See Also == | ||
Latest revision as of 01:01, 13 January 2019
Problem
In the figure there are 
line segments drawn from
vertex 
to the base 
(not counting the segments 
or 
).
![[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]](http://latex.artofproblemsolving.com/0/1/2/012fc4457f36f81cdf88876917f2cd36048e3faa.png)
(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
(a) 
(b) 
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 | ||
