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Triangle in Base of Cone

Source:

March 23, 2008
geometry3D geometrytetrahedronpyramidsimilar triangles

Problem Statement

Consider a circular cone with vertex V V, and let ABC ABC be a triangle inscribed in the base of the cone, such that AB AB is a diameter and AC \equal{} BC. Let L L be a point on BV BV such that the volume of the cone is 4 times the volume of the tetrahedron ABCL ABCL. Find the value of BL/LV BL/LV.
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