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Swedish Mathematical Competition
1992 Swedish Mathematical Competition
5
5
Part of
1992 Swedish Mathematical Competition
Problems
(1)
right triangle if a^2 + b^2 = 2cR
Source: 1992 Swedish Mathematical Competition p5
4/2/2021
A triangle has sides
a
,
b
,
c
a, b, c
a
,
b
,
c
with longest side
c
c
c
, and circumradius
R
R
R
. Show that if
a
2
+
b
2
=
2
c
R
a^2 + b^2 = 2cR
a
2
+
b
2
=
2
c
R
, then the triangle is right-angled.
right triangle
right angle
geometry
circumradius