MathDB
Problems
Contests
International Contests
Cono Sur Olympiad
Cono Sur Shortlist - geometry
2003.G3
2003.G3
Part of
Cono Sur Shortlist - geometry
Problems
(1)
computational in a square, a^2 = b^2 + c^2, right angle wanted
Source: 2003 Cono Sur Shortlist G3
7/26/2019
An interior
P
P
P
point to a square
A
B
C
D
ABCD
A
BC
D
is such that
P
A
=
a
,
P
B
=
b
PA = a, PB = b
P
A
=
a
,
PB
=
b
and
P
C
=
b
+
c
PC = b + c
PC
=
b
+
c
, where the numbers
a
,
b
a, b
a
,
b
and
c
c
c
satisfy the relationship
a
2
=
b
2
+
c
2
a^2 = b^2 + c^2
a
2
=
b
2
+
c
2
. Prove that the angle
B
P
C
BPC
BPC
is right.
square
geometry
right angle