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Omni-MATH / Let ABC be an acute scalene triangle with circumcenter O and centroid G. Given that AGO is a right triangle, AO=9, and BC=15, let S be the sum of all possible values for the area o…

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problem

Let ABCA B C be an acute scalene triangle with circumcenter OO and centroid GG. Given that AGOA G O is a right triangle, AO=9A O=9, and BC=15B C=15, let SS be the sum of all possible values for the area of triangle AGOA G O. Compute S2S^{2}.
Plain-text mathematical notation (without MathML)
Let ABC be an acute scalene triangle with circumcenter O and centroid G. Given that AGO is a right triangle, AO=9, and BC=15, let S be the sum of all possible values for the area of triangle AGO. Compute S².
Original LaTeX notation
Let $A B C$ be an acute scalene triangle with circumcenter $O$ and centroid $G$. Given that $A G O$ is a right triangle, $A O=9$, and $B C=15$, let $S$ be the sum of all possible values for the area of triangle $A G O$. Compute $S^{2}$.

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Source and history

task_id
20e023a3-16be-5281-bb98-57b317f9bae6
task_key
test--20e023a3-16be-5281-bb98-57b317f9bae6
task_revision_id
1
config / split
/ test

Official source

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