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National and Regional Contests
India Contests
India National Olympiad
2021 India National Olympiad
5
5
Part of
2021 India National Olympiad
Problems
(1)
Incredible vanilla geometry again
Source: INMO 2021 Problem 5
3/7/2021
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
,
∠
A
B
D
=
3
0
∘
\angle ABD=30^\circ
∠
A
B
D
=
3
0
∘
,
∠
B
C
A
=
7
5
∘
\angle BCA=75^\circ
∠
BC
A
=
7
5
∘
,
∠
A
C
D
=
2
5
∘
\angle ACD=25^\circ
∠
A
C
D
=
2
5
∘
and
C
D
=
C
B
CD=CB
C
D
=
CB
. Extend
C
B
CB
CB
to meet the circumcircle of triangle
D
A
C
DAC
D
A
C
at
E
E
E
. Prove that
C
E
=
B
D
CE=BD
CE
=
B
D
.Proposed by BJ Venkatachala
geometry
angles
Equilateral Triangle
equal lengths
INMO
trigonometry