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Indonesia Regional MO OSP SMA - geometry
2015.3
2015.3
Part of
Indonesia Regional MO OSP SMA - geometry
Problems
(1)
<BAC = 2< DPC wanted, BD = 2DC and <BAC = <BPD given
Source: 2015 Indonesia MO Province P2 q3 OSP
12/10/2020
Given the isosceles triangle
A
B
C
ABC
A
BC
, where
A
B
=
A
C
AB = AC
A
B
=
A
C
. Let
D
D
D
be a point in the segment
B
C
BC
BC
so that
B
D
=
2
D
C
BD = 2DC
B
D
=
2
D
C
. Suppose also that point
P
P
P
lies on the segment
A
D
AD
A
D
such that:
∠
B
A
C
=
∠
B
P
D
\angle BAC = \angle BP D
∠
B
A
C
=
∠
BP
D
. Prove that
∠
B
A
C
=
2
∠
D
P
C
\angle BAC = 2\angle DP C
∠
B
A
C
=
2∠
D
PC
.
geometry
equal angles
equal segments
Equilateral