Chapter 8.2, Problem 57E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# A cyclic quadrilateral has lengths of sides 25, 39, 52, and 60 (in that order).a) Show that, for some choice of lengths a ,   b ,   c , and d , a 2 + b 2 =   c 2 + d 2 . b) Use the formula from Exercise 56 to find the area of this cyclic quadrilateral.

To determine

(a)

To Show:

Cyclic quadrilateral satisfies the condition a2+b2=c2+d2 for the choice of lengths of sides 25, 39, 52, and 60.

Explanation

Formula Used:

The area of the quadrilateral MNPQ is A=ab+cd2 if it is a cyclic quadrilateral with sides a,b,c and d which satisfies the condition a2+b2=c2+d2.

It is given that the cyclic quadrilateral has lengths of sides 25, 39, 52, and 60.

Cyclic quadrilateral satisfies the condition a2+b2=c2+d2 for the choice of lengths of sides 25, 39, 52, and 60.

Since the lengths are given in increasing order, we need to consider the smallest and largest values as a and b. The remaining mid values goes to c and d.

Therefore, a=25,b=60,c=39 and d=52

To determine

(b)

To find:

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