2016 AMC 10A Problems/Problem 21
Revision as of 23:11, 3 February 2016 by Awesomeclaw (talk | contribs)
Circles with centers and
, having radii
and
, respectively, lie on the same side of line
and are tangent to
at
and
, respectively, with
between
and
. The circle with center
is externally tangent to each of the other two circles. What is the area of triangle
?
==Solution==[edit]
Notice that we can find in two different ways:
and
, so
Thus, these are equal. . Additionally,
. Therefore,
. Similarly,
. We can calculate
easily because
.
.
Plugging into first equation, the two sums of areas, .
.