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International Contests
IMO Longlists
1990 IMO Longlists
83
83
Part of
1990 IMO Longlists
Problems
(1)
Prove that S(ABC)=AD^2 - ILL 1990 SWE1
Source:
9/19/2010
Point
D
D
D
is on the hypotenuse
B
C
BC
BC
of right-angled triangle
A
B
C
ABC
A
BC
. The inradii of triangles
A
D
B
ADB
A
D
B
and
A
D
C
ADC
A
D
C
are equal. Prove that
S
A
B
C
=
A
D
2
S_{ABC} = AD^2
S
A
BC
ā
=
A
D
2
, where
S
S
S
is the area function.
geometry
geometry unsolved