Difference between revisions of "1979 USAMO Problems/Problem 2"
Danielguo94 (talk | contribs) |
Danielguo94 (talk | contribs) |
||
| Line 3: | Line 3: | ||
<math>N</math> is the north pole. <math>A</math> and <math>B</math> are points on a great circle through <math>N</math> equidistant from <math>N</math>. <math>C</math> is a point on the equator. Show that the great circle through <math>C</math> and <math>N</math> bisects the angle <math>ACB</math> in the spherical triangle <math>ABC</math> (a spherical triangle has great circle arcs as sides). | <math>N</math> is the north pole. <math>A</math> and <math>B</math> are points on a great circle through <math>N</math> equidistant from <math>N</math>. <math>C</math> is a point on the equator. Show that the great circle through <math>C</math> and <math>N</math> bisects the angle <math>ACB</math> in the spherical triangle <math>ABC</math> (a spherical triangle has great circle arcs as sides). | ||
| + | ==Solution== | ||
| + | {{solution}} | ||
| + | |||
| + | ==See also== | ||
{{USAMO box|year=1979|num-b=1|num-a=3}} | {{USAMO box|year=1979|num-b=1|num-a=3}} | ||
Revision as of 22:46, 11 April 2012
Problem
is the north pole. 
and 
are points on a great circle through equidistant from . 
is a point on the equator. Show that the great circle through and bisects the angle 
in the spherical triangle 
(a spherical triangle has great circle arcs as sides).
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1979 USAMO (Problems • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
