91Ó°ÊÓ

Two cones with a common vertex which have a common generatrix and the same tangent plane passing through it are called tangent. Prove that two tangent cones have a common symmetry plane.

Compute the volume and the lateral surface area of a conical frustum that has the generatrix \(15 \mathrm{~cm}\) long, and the radii of the bases \(18 \mathrm{~cm}\) and \(27 \mathrm{~cm}\).

On the surface of a given ball, find the geometric locus of the tangency points with lines drawn from a given point outside the ball and tangent to the sphere.