Difference between revisions of "2015 AIME I Problems/Problem 6"
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This means that: | This means that: | ||
− | + | <math>180-3x/2=180-3y/2+12</math>, | |
− | + | which when simplified yields <math>3x/2+12=3y/2</math>, or <math>x+8=y</math>. | |
Since: | Since: | ||
<math>5y=180-2x</math>, <math>5x+40=180-2x</math> | <math>5y=180-2x</math>, <math>5x+40=180-2x</math> |
Revision as of 10:31, 21 March 2015
Problem
Point and
are equally spaced on a minor arc of a cirle. Points
and
are equally spaced on a minor arc of a second circle with center
as shown in the figure below. The angle
exceeds
by
. Find the degree measure of
.
Solution
Let be the center of the circle with
on it.
Let and
.
is therefore
by way of circle
and
by way of circle
.
is
by way of circle
, and
is
by way of circle
.
This means that:
,
which when simplified yields , or
.
Since:
,
So:
is equal to
+
, which equates to
.
Plugging in yields
, or
See Also
2015 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.