Question

Why sphere is fitted half the height into the cone?

Answer 1

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Since this is the largest possible sphere inside the cone the sphere touches the cone at E and thus AB is a tangent to the sphere at E and hence angle DEB is a right angle. Thus the triangles DEB and ABC have one angle in common, angle EBC, and each has a right angle, angles DEB and BCA. Thus angles BDE and CAD are congruent and hence triangles DEB and ABC are similar. Therefore

|BD|/|DE| = |AB|/|CA|.




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