1995 AHSME Problems/Problem 17: Difference between revisions
New page: ==Problem== Given regular pentagon <math>ABCDE</math>, a circle can be drawn that is tangent to <math>\overline{DC}</math> at <math>D</math> and to <math>\overline{AB}</math> at <math>A</m... |
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==See also== | ==See also== | ||
{{AHSME box|year=1995|num-b=16|num-a=18}} | |||
[[Category:Introductory Geometry Problems]] | [[Category:Introductory Geometry Problems]] | ||
Revision as of 11:05, 29 September 2008
Problem
Given regular pentagon 
, a circle can be drawn that is tangent to 
at 
and to 
at 
. The number of degrees in minor arc 
is
Solution
Define major arc DA as DA, and minor arc DA as da. Extending DC and AB to meet at F, we see that 
. We now have two equations: 
, and 
. Solving, 
and 
.
See also
| 1995 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
