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2018 Stanford Mathematics Tournament
8
8
Part of
2018 Stanford Mathematics Tournament
Problems
(1)
SMT 2018 Geometry #8 right triangle
Source:
8/8/2023
Let
A
B
C
ABC
A
BC
be a right triangle with
∠
A
C
B
=
9
0
o
\angle ACB = 90^o
∠
A
CB
=
9
0
o
,
B
C
=
16
BC = 16
BC
=
16
, and
A
C
=
12
AC = 12
A
C
=
12
. Let the angle bisectors of
∠
B
A
C
\angle BAC
∠
B
A
C
and
∠
A
B
C
\angle ABC
∠
A
BC
intersect
B
C
BC
BC
and
A
C
AC
A
C
at
D
D
D
and
E
E
E
respectively. Let
A
D
AD
A
D
and
B
E
BE
BE
intersect at
I
I
I
, and let the circle centered at
I
I
I
passing through
C
C
C
intersect
A
B
AB
A
B
at
P
P
P
and
Q
Q
Q
such that
A
Q
<
A
P
AQ < AP
A
Q
<
A
P
. Compute the area of quadrilateral
D
P
Q
E
DP QE
D
PQE
.
geometry