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Omni-MATH / Let ABC be a triangle with AB=3,BC=4, and CA=5. Let A₁,A₂ be points on side BC, B₁,B₂ be points on side CA, and C₁,C₂ be points on side AB. Suppose that there exists a point P such…

Problem

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problem

Let ABCA B C be a triangle with AB=3,BC=4A B=3, B C=4, and CA=5C A=5. Let A1,A2A_{1}, A_{2} be points on side BCB C, B1,B2B_{1}, B_{2} be points on side CAC A, and C1,C2C_{1}, C_{2} be points on side ABA B. Suppose that there exists a point PP such that PA1A2,PB1B2P A_{1} A_{2}, P B_{1} B_{2}, and PC1C2P C_{1} C_{2} are congruent equilateral triangles. Find the area of convex hexagon A1A2B1B2C1C2A_{1} A_{2} B_{1} B_{2} C_{1} C_{2}.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=3,BC=4, and CA=5. Let A₁,A₂ be points on side BC, B₁,B₂ be points on side CA, and C₁,C₂ be points on side AB. Suppose that there exists a point P such that PA₁A₂,PB₁B₂, and PC₁C₂ are congruent equilateral triangles. Find the area of convex hexagon A₁A₂B₁B₂C₁C₂.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=3, B C=4$, and $C A=5$. Let $A_{1}, A_{2}$ be points on side $B C$, $B_{1}, B_{2}$ be points on side $C A$, and $C_{1}, C_{2}$ be points on side $A B$. Suppose that there exists a point $P$ such that $P A_{1} A_{2}, P B_{1} B_{2}$, and $P C_{1} C_{2}$ are congruent equilateral triangles. Find the area of convex hexagon $A_{1} A_{2} B_{1} B_{2} C_{1} C_{2}$.

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Source and history

task_id
0e098a16-2e63-5d4d-8c0b-a55dd1817e20
task_key
test--0e098a16-2e63-5d4d-8c0b-a55dd1817e20
task_revision_id
1
config / split
/ test

Official source

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