   Chapter 8.3, Problem 36E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# 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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