Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 10"
Vanstraelen (talk | contribs) (→Solution) |
m |
||
Line 3: | Line 3: | ||
==Solution== | ==Solution== | ||
− | |||
Latest revision as of 23:58, 24 April 2013
Problem
In ,
,
, and
have lengths
,
, and
, respectively. Let the incircle, circle
, of
touch
,
, and
at
,
, and
, respectively. Construct three circles,
,
, and
, externally tangent to the other two and circles
,
, and
are internally tangent to the circle
at
,
, and
, respectively. Let circles
,
,
, and
have radii
,
,
, and
, respectively. If
where
and
are positive integers, find
.
Solution
Radius , radius
, radius
and
, see picture.
Given , so
.