The figure below shows
a triangle ABC with the
incircle I.
Circle A_{1} with a chord BC cuts circle I
at A_{2} and A_{3}. Circle B_{1} with a
chord AC cuts circle I
at B_{2} and B_{3}. Circle C_{1} with a chord AB cuts circle I
at C_{2} and C_{3}. Lines A_{2}A_{3} and
BC meet at A_{4}. Lines B_{2}B_{3} and AC meet at
B_{4}. Lines C_{2}C_{3} and BA meet at C_{4}.
Prove that C_{4}, A_{4}, and B_{4} are
collinear.

Geometry Problems

Ten problems: 1341-1350

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Chord

Intersecting Circles Index

Collinear Points

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