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Omni-MATH / Let ABC be an equilateral triangle of side length 6 inscribed in a circle ω. Let A₁,A₂ be the points (distinct from A) where the lines through A passing through the two trisection …

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problem

Let ABCABC be an equilateral triangle of side length 6 inscribed in a circle ω\omega. Let A1,A2A_{1}, A_{2} be the points (distinct from AA) where the lines through AA passing through the two trisection points of BCBC meet ω\omega. Define B1,B2,C1,C2B_{1}, B_{2}, C_{1}, C_{2} similarly. Given that A1,A2,B1,B2,C1,C2A_{1}, A_{2}, B_{1}, B_{2}, C_{1}, C_{2} appear on ω\omega in that order, find the area of hexagon A1A2B1B2C1C2A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}.
Plain-text mathematical notation (without MathML)
Let ABC be an equilateral triangle of side length 6 inscribed in a circle ω. Let A₁,A₂ be the points (distinct from A) where the lines through A passing through the two trisection points of BC meet ω. Define B₁,B₂,C₁,C₂ similarly. Given that A₁,A₂,B₁,B₂,C₁,C₂ appear on ω in that order, find the area of hexagon A₁A₂B₁B₂C₁C₂.
Original LaTeX notation
Let $ABC$ be an equilateral triangle of side length 6 inscribed in a circle $\omega$. Let $A_{1}, A_{2}$ be the points (distinct from $A$) where the lines through $A$ passing through the two trisection points of $BC$ meet $\omega$. Define $B_{1}, B_{2}, C_{1}, C_{2}$ similarly. Given that $A_{1}, A_{2}, B_{1}, B_{2}, C_{1}, C_{2}$ appear on $\omega$ in that order, find the area of hexagon $A_{1}A_{2}B_{1}B_{2}C_{1}C_{2}$.

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Source and history

task_id
eaa81591-7e61-5866-a768-f14a16d826e1
task_key
test--eaa81591-7e61-5866-a768-f14a16d826e1
task_revision_id
1
config / split
/ test

Official source

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