Difference between revisions of "1979 USAMO Problems/Problem 2"
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<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). | ||
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| + | {{USAMO box|year=1979|before=1|num-a=3}} | ||
Revision as of 22:42, 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).
| 1979 USAMO (Problems • Resources) | ||
| Preceded by 1 |
Followed by Problem 3 | |
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| All USAMO Problems and Solutions | ||
