A point
inside a regular tetrahedron is such that its distance from all vertices
&
of the tetrahedron is the same. The line
, when produced, intersects the plane formed by vertices
&
at the point
. The ratio
can be written as
.
Find .
Try more from my set Geometry Problems .
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Note that A P is the radius of the circumsphere, and A Q is the height of the tetrahedron. Then A Q A P = ( 3 a 6 ) ( 4 a 6 ) = 4 3 so b a = 4 3 . Assuming the author meant that A Q A P can be written as b a where a and b are positive coprime integers, this means a = 3 and b = 4 . Finally 3 4 = 8 1