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MathLinks Contest 5th
1.3
1.3
Part of
MathLinks Contest 5th
Problems
(1)
0513 geometry 5th edition Round 1 p3
Source:
5/6/2021
Let
A
B
C
ABC
A
BC
be a triangle and let
A
′
∈
B
C
A' \in BC
A
′
∈
BC
,
B
′
∈
C
A
B' \in CA
B
′
∈
C
A
and
C
′
∈
A
B
C' \in AB
C
′
∈
A
B
be three collinear points. a) Prove that each pair of circles of diameters
A
A
′
AA'
A
A
′
,
B
B
′
BB'
B
B
′
and
C
C
′
CC'
C
C
′
has the same radical axis; b) Prove that the circumcenter of the triangle formed by the intersections of the lines
A
A
′
,
B
B
′
AA' , BB'
A
A
′
,
B
B
′
and
C
C
′
CC'
C
C
′
lies on the common radical axis found above.
geometry
5th edition