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Omni-MATH / Let ABC be a triangle and D,E, and F be the midpoints of sides BC,CA, and AB respectively. What is the maximum number of circles which pass through at least 3 of these 6 points?

Problem

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problem

Let ABCA B C be a triangle and D,ED, E, and FF be the midpoints of sides BC,CAB C, C A, and ABA B respectively. What is the maximum number of circles which pass through at least 3 of these 6 points?
Plain-text mathematical notation (without MathML)
Let ABC be a triangle and D,E, and F be the midpoints of sides BC,CA, and AB respectively. What is the maximum number of circles which pass through at least 3 of these 6 points?
Original LaTeX notation
Let $A B C$ be a triangle and $D, E$, and $F$ be the midpoints of sides $B C, C A$, and $A B$ respectively. What is the maximum number of circles which pass through at least 3 of these 6 points?

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Source and history

task_id
fb37b06f-1a28-5c2c-a95b-0fb92fb5bfb7
task_key
test--fb37b06f-1a28-5c2c-a95b-0fb92fb5bfb7
task_revision_id
1
config / split
/ test

Official source

initial import