Problem 8. Let CCR" be a closed convex set, and suppose that X₁,..., XK are on the boundary of C. Suppose that for each i, a (x - x₁) = 0 defines a supporting hyperplane for Cat x₁, i.e., C C {x | a (x - x) ≤0}. Consider the two polyhedra Pinner = conv{X₁,..., XK}, Pouter = {x|al(x − xi) ≤ 0, i = 1,..., K}. - Show that Pinner CCC Pouter. Draw a picture to explain this.

Problem 8. Let CCR" be a closed convex set, and suppose that X₁,..., XK are on the boundary of C. Suppose that for each i, a (x - x₁) = 0 defines a supporting hyperplane for Cat x₁, i.e., C C {x | a (x - x) ≤0}. Consider the two polyhedra Pinner = conv{X₁,..., XK}, Pouter = {x|al(x − xi) ≤ 0, i = 1,..., K}. - Show that Pinner CCC Pouter. Draw a picture to explain this.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.CR: Review Exercises

Problem 38CR: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of...

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