MathDB
Problems
Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1985 Swedish Mathematical Competition
3
3
Part of
1985 Swedish Mathematical Competition
Problems
(1)
DE = r wanted, inscribed isosceles ABC, equilateral BCD
Source: 1985 Swedish Mathematical Competition p3
3/28/2021
Points
A
,
B
,
C
A,B,C
A
,
B
,
C
with
A
B
=
B
C
AB = BC
A
B
=
BC
are given on a circle with radius
r
r
r
, and
D
D
D
is a point inside the circle such that the triangle
B
C
D
BCD
BC
D
is equilateral. The line
A
D
AD
A
D
meets the circle again at
E
E
E
. Show that
D
E
=
r
DE = r
D
E
=
r
.
geometry
isosceles
Equilateral