MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
USAJMO
2019 USAJMO
3
3
Part of
2019 USAJMO
Problems
(1)
The best length condition you'll ever see
Source: USAMO 2019 Problem 2 and JMO 2019 Problem 3, by Ankan Bhattacharya
4/17/2019
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral satisfying
A
D
2
+
B
C
2
=
A
B
2
AD^2 + BC^2 = AB^2
A
D
2
+
B
C
2
=
A
B
2
. The diagonals of
A
B
C
D
ABCD
A
BC
D
intersect at
E
E
E
. Let
P
P
P
be a point on side
A
B
‾
\overline{AB}
A
B
satisfying
∠
A
P
D
=
∠
B
P
C
\angle APD = \angle BPC
∠
A
P
D
=
∠
BPC
. Show that line
P
E
PE
PE
bisects
C
D
‾
\overline{CD}
C
D
.Proposed by Ankan Bhattacharya
USA(J)MO
USAMO
Hi