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Omni-MATH / In △ABC,ω is the circumcircle, I is the incenter and I_(A) is the A-excenter. Let M be the midpoint of arc (BAC)^ on ω, and suppose that X,Y are the projections of I onto MI_(A) an…

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problem

In △ABC,ω\triangle A B C, \omega is the circumcircle, II is the incenter and IAI_{A} is the AA-excenter. Let MM be the midpoint of arc BAC^\widehat{B A C} on ω\omega, and suppose that X,YX, Y are the projections of II onto MIAM I_{A} and IAI_{A} onto MIM I, respectively. If △XYIA\triangle X Y I_{A} is an equilateral triangle with side length 1, compute the area of △ABC\triangle A B C.
Plain-text mathematical notation (without MathML)
In △ABC,ω is the circumcircle, I is the incenter and I_(A) is the A-excenter. Let M be the midpoint of arc (BAC)^ on ω, and suppose that X,Y are the projections of I onto MI_(A) and I_(A) onto MI, respectively. If △XYI_(A) is an equilateral triangle with side length 1, compute the area of △ABC.
Original LaTeX notation
In $\triangle A B C, \omega$ is the circumcircle, $I$ is the incenter and $I_{A}$ is the $A$-excenter. Let $M$ be the midpoint of arc $\widehat{B A C}$ on $\omega$, and suppose that $X, Y$ are the projections of $I$ onto $M I_{A}$ and $I_{A}$ onto $M I$, respectively. If $\triangle X Y I_{A}$ is an equilateral triangle with side length 1, compute the area of $\triangle A B C$.

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task_id
4cd5f31c-4760-5eac-b047-aa061cf778bd
task_key
test--4cd5f31c-4760-5eac-b047-aa061cf778bd
task_revision_id
1
config / split
/ test

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