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Omni-MATH / In the triangle △ABC, let G be the centroid, and let I be the center of the inscribed circle. Let α and β be the angles at the vertices A and B, respectively. Suppose that the segm…

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problem

In the triangle △ABC\triangle ABC, let GG be the centroid, and let II be the center of the inscribed circle. Let α\alpha and β\beta be the angles at the vertices AA and BB, respectively. Suppose that the segment IGIG is parallel to ABAB and that β=2tan−1(1/3)\beta = 2 \tan^{-1} (1/3). Find α\alpha.
Plain-text mathematical notation (without MathML)
In the triangle △ABC, let G be the centroid, and let I be the center of the inscribed circle. Let α and β be the angles at the vertices A and B, respectively. Suppose that the segment IG is parallel to AB and that β=2tan^(−1)(1/3). Find α.
Original LaTeX notation
In the triangle $\triangle ABC$, let $G$ be the centroid, and let $I$ be the center of the inscribed circle. Let $\alpha$ and $\beta$ be the angles at the vertices $A$ and $B$, respectively. Suppose that the segment $IG$ is parallel to $AB$ and that $\beta = 2 \tan^{-1} (1/3)$. Find $\alpha$.

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Source and history

task_id
c0f6ba75-ca21-52ba-9c7a-1b630df77c54
task_key
test--c0f6ba75-ca21-52ba-9c7a-1b630df77c54
task_revision_id
1
config / split
/ test

Official source

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