Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
bartleby

Videos

Question
Book Icon
Chapter 16.4, Problem 2PS
To determine

To find: the distance between EF if point F is located in the exterior of the square.

Expert Solution & Answer
Check Mark

Answer to Problem 2PS

The distance, between EF is 72 .

Explanation of Solution

Given:

  Geometry For Enjoyment And Challenge, Chapter 16.4, Problem 2PS

  AF=6 and BF=8 .

Concept used:

Ptolemy’s theorem:

For a cyclic quadrilateral or quadrilateral which inscribe in a circle then the sum of the products of the two pairs opposite side equals the product of the diagonal.

Mathematically,

  AC.BD=AB.CD+AD.BC .

Pythagoras theorem:

  H2=P2+B2 .

Calculation:

Using Pythagoras theorem:

  (AB)2=(AF)2+(BF)2.(AB)2=(6)2+(8)2.(AB)2=36+64.AB=10.

Since, square has equal side BC=AB=BD=AD=10 .

Again, using Pythagoras theorem ΔABD :

  AC=102+102=102.AE=AC2=1022=52.

Similarly, BE=52.

Using Ptolemy’s theorem.

  AB×EF=AF×BE+BF×AE.10×EF=6(52)+8(52).EF=72.

Hence, the distance, between EF is 72 .

Knowledge Booster
Background pattern image
Geometry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Text book image
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning
Quadrilaterals: Missing Angles and Sides; Author: rhornfeck;https://www.youtube.com/watch?v=knVj1O0L2TM;License: Standard YouTube License, CC-BY
STD IX | State Board | Types of Quadrilateral; Author: Robomate;https://www.youtube.com/watch?v=wh0KQ4UB0EU;License: Standard YouTube License, CC-BY