In tetrahedron ABCD altitudes AA', BB',CC',DD' intersects in one point. O is a centre of sphere circumscribed on ABCD.Prove that if DO is perpendicular to plane A'B'C' then triangle ABC is equilateral. Please hint.

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- Oct 1st 2011, 05:51 AMgreg1987prove that triangle is equilateral
In tetrahedron ABCD altitudes AA', BB',CC',DD' intersects in one point. O is a centre of sphere circumscribed on ABCD.Prove that if DO is perpendicular to plane A'B'C' then triangle ABC is equilateral. Please hint.

- Oct 3rd 2011, 12:07 AMmathbyteRe: prove that triangle is equilateral