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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2003 All-Russian Olympiad Regional Round
11.2
11.2
Part of
2003 All-Russian Olympiad Regional Round
Problems
(1)
<KDA = <BCA or <KDA = <KBA. if KD = DC, <BAC = 1/2 <KDC,<DAC = 1/2<KB
Source: - All-Russian MO 2003 Regional (R4) 11.2
9/17/2024
On the diagonal
A
C
AC
A
C
of a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
is chosen such a point
K
K
K
such that
K
D
=
D
C
KD = DC
KD
=
D
C
,
∠
B
A
C
=
1
2
∠
K
D
C
\angle BAC = \frac12 \angle KDC
∠
B
A
C
=
2
1
∠
KD
C
,
∠
D
A
C
=
1
2
∠
K
B
C
\angle DAC = \frac12 \angle KBC
∠
D
A
C
=
2
1
∠
K
BC
. Prove that
∠
K
D
A
=
∠
B
C
A
\angle KDA = \angle BCA
∠
KD
A
=
∠
BC
A
or
∠
K
D
A
=
∠
K
B
A
\angle KDA = \angle KBA
∠
KD
A
=
∠
K
B
A
.
geometry
angles
equal angles