   Chapter 5.6, Problem 30E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given point D in the interior of Δ R S T , suppose that R G = 2 , G S = 3 , S H = 3 and H T = 4. Find K T K R . To determine

To find:

The value of KTKR.

Explanation

Given:

Consider a point D in the interior of ΔRST and RG=2,GS=3,SH=3,HT=4.

Theorem used:

Ceva’s theorem:

Let point D be any point in the interior of ΔABC, where E, F, and G lie on ΔABC, let BE¯,AF¯ and CG¯ be the line segments determined by D and vertices of ΔABC. Then the product of the ratios of the lengths of the segments of each of the three sides (taken in order from a given vertex of the triangle) equals 1; that is AGGBBFFCCEEA=1.

Calculation:

Let D be a point in the interior of ΔRST.

By Ceva’s theorem, we get RGGSSHHTKTKR=1

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