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Regional Mathematical Olympiad
2024 India Regional Mathematical Olympiad
5
RMO KV 2024 Q5
RMO KV 2024 Q5
Source: RMO KV 2024 Q5
November 3, 2024
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
∠
A
B
C
=
2
0
∘
\angle ABC = 20^{\circ}
∠
A
BC
=
2
0
∘
and
∠
A
C
B
=
4
0
∘
\angle ACB = 40^{\circ}
∠
A
CB
=
4
0
∘
. Let
D
D
D
be a point on
B
C
BC
BC
such that
∠
B
A
D
=
∠
D
A
C
\angle BAD = \angle DAC
∠
B
A
D
=
∠
D
A
C
. Let the incircle of triangle
A
B
C
ABC
A
BC
touch
B
C
BC
BC
at
E
E
E
. Prove that
B
D
=
2
⋅
C
E
BD = 2 \cdot CE
B
D
=
2
⋅
CE
.
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