MathDB

ABC

Source: SRMO 2005

April 10, 2005

geometrycircumcircletrigonometrypower of a pointradical axissimilar trianglesgeometry proposed

Problem Statement

Assume

A,B,C

are three collinear points that

B \in [AC]

. Suppose

AA'

and

BB'

are to parrallel lines that

A'

,

B'

and

C

are not collinear. Suppose

O_1

is circumcenter of circle passing through

A

,

A'

and

C

. Also

O_2

is circumcenter of circle passing through

B

,

B'

and

C

. If area of

A'CB'

is equal to area of

O_1CO_2

, then find all possible values for

\angle CAA'

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