Mock AIME 4 2006-2007 Problems/Problem 4
Problem
Points ,
, and
are on the circumference of a unit circle so that the measure of
is
, the measure of
is
, and the measure of
is
. The area of the triangular shape bounded by
and line segments
and
can be written in the form
, where
and
are relatively prime positive integers. Find
.
Solution
Let the center of the circle be . The area of the desired region is easily seen to be that of sector
plus the area of triangle
minus the area of triangle
. Using the area formula
to compute the areas of the two triangles, this is
, so the answer is
.
See also
Mock AIME 4 2006-2007 (Problems, Source) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |