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Omni-MATH / Circle ω is inscribed in rhombus HM₁M₂T so that ω is tangent to (HM₁)¯ at A,(M₁M₂)¯ at I,(M₂T)¯ at M, and (TH)¯ at E. Given that the area of HM₁M₂T is 1440 and the area of EMT is 4…

Problem

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problem

Circle ω\omega is inscribed in rhombus HM1M2TH M_{1} M_{2} T so that ω\omega is tangent to HM1¯\overline{H M_{1}} at A,M1M2¯A, \overline{M_{1} M_{2}} at I,M2T¯I, \overline{M_{2} T} at MM, and TH¯\overline{T H} at EE. Given that the area of HM1M2TH M_{1} M_{2} T is 1440 and the area of EMTE M T is 405 , find the area of AIMEA I M E.
Plain-text mathematical notation (without MathML)
Circle ω is inscribed in rhombus HM₁M₂T so that ω is tangent to (HM₁)¯ at A,(M₁M₂)¯ at I,(M₂T)¯ at M, and (TH)¯ at E. Given that the area of HM₁M₂T is 1440 and the area of EMT is 405 , find the area of AIME.
Original LaTeX notation
Circle $\omega$ is inscribed in rhombus $H M_{1} M_{2} T$ so that $\omega$ is tangent to $\overline{H M_{1}}$ at $A, \overline{M_{1} M_{2}}$ at $I, \overline{M_{2} T}$ at $M$, and $\overline{T H}$ at $E$. Given that the area of $H M_{1} M_{2} T$ is 1440 and the area of $E M T$ is 405 , find the area of $A I M E$.

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Source and history

task_id
bab5bd72-e7bd-5efd-a300-0ca65c59989b
task_key
test--bab5bd72-e7bd-5efd-a300-0ca65c59989b
task_revision_id
1
config / split
/ test

Official source

initial import