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Singapore Junior Math Olympiad
2019 Singapore Junior Math Olympiad
1
1
Part of
2019 Singapore Junior Math Olympiad
Problems
(1)
AE=2EB inside a right isosceles triangle (Singapore Junior 2019)
Source:
7/10/2019
In the triangle
A
B
C
,
A
C
=
B
C
,
∠
C
=
9
0
o
,
D
ABC, AC=BC, \angle C=90^o, D
A
BC
,
A
C
=
BC
,
∠
C
=
9
0
o
,
D
is the midpoint of
B
C
,
E
BC, E
BC
,
E
is the point on
A
B
AB
A
B
such that
A
D
AD
A
D
is perpendicular to
C
E
CE
CE
. Prove that
A
E
=
2
E
B
AE=2EB
A
E
=
2
EB
.
geometry
right triangles
Isosceles Triangle
isosceles