# Chapter 13: Chapter 13

Problem 252

Given; \(\underline{A D}\) is an angle bisector of \(\triangle \mathrm{ABC} ;\) point \(\mathrm{E}\) is on \(\underline{\mathrm{AD}}\) such that $\mathrm{AB} \cdot \mathrm{AC}=\mathrm{AD} \cdot \mathrm{AE}\(. Proves \)\phi \mathrm{B} \cong<\mathrm{AEC}$.

Problem 255

In the accompanying figure, points \(D, E\), and \(F\) are points on the triangle \(\triangle \mathrm{ABC}\) such that $\underline{\mathrm{AD}}, \underline{\mathrm{BE}}\(, and \)\underline{\mathrm{CF}}$ are concurrent at point P. Show that $$ (\mathrm{BD} / \mathrm{DC})(\mathrm{CE} / \mathrm{EA})(\mathrm{AF} / \mathrm{FB})=1 $$

Problem 256

The lengths of the radii of two circles are 15 in. and 5 in. Find the ratio of the circumferences of the two circles.

Problem 257

Prove that any two regular polygons with the same number of sides are similar.

Problem 258

Show that a regular pentagon and the pentagon determined by joining all the vertices of the regular pentagon are similar.

Problem 259

The lengths of two corresponding sides of two similar polygons are 4 and 7 . If the perimeter of the smaller polygon is 20 , find the perimeter of the larger polygon.