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3d geometry

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The midpoints of two sides of a triangle 2009-03-17
From Manis:
Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it.
Answered by Robert Dawson.
A plane cuts a line segment 2009-03-17
From Manis:
Find the ratio in which the line joining (2,4,16) and (3,5,-4) is divided by the plane 2x-3y+z+6=0.
Answered by Robert Dawson.
A sphere in a cube 2006-11-09
From Lukas:
Given a cube and a cross diagonal, what is the largest size sphere that fits in the cube and does not touch or intersect the cross diagonal?
Answered by Steve La Rocque, Penny Nom and Walter Whiteley.
 
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