2021 Fall AMC 12B Problems/Problem 9
Solution 1 (Cosine Rule)
Construct the circle that passes through ,
, and
, centered at
.
Then connect , and notice that
is the perpendicular bisector of
. Let the intersection of
with
be
.
Also notice that and
are the angle bisectors of angle
and
respectively. We then deduce
.
Consider another point on Circle
opposite to point
.
As an inscribed quadrilateral of Circle
,
.
Afterward, deduce that .
By the Cosine Rule, we have the equation: (where is the radius of circle
)
The area is therefore .
~Wilhelm Z