   Chapter 8.3, Problem 38E 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

Consider regular pentagon R S T V Q (not shown). Given that diagonals Q T ¯ and V R ¯ intersect at point F , show that V F · F R = T F · F Q .

To determine

To prove:

VF·FR=TF·FQ, if the diagonals QT¯ and VR¯ intersect at point F in regular pentagon RSTVQ.

The measure of VPS.

Explanation

Theorem used:

Intersecting chord theorem:

“When two chords intersect each other inside the circle, then the products of their segments are equal.”

Given,

The regular pentagon RSTVQ

and the diagonals QT¯ and VR¯ intersect at point F in regular pentagon RSTVQ

Draw a circle such that the regular pentagon inscribed in a circle.

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