SOLUTION: Please help me solve this problem: A cyclic quadrilateral has sides 5 cm, 4 cm, 7 cm, and 10 cm. Find the area of the quadrilateral. Find also the radius of the circumscribed ci

Algebra ->  Rectangles -> SOLUTION: Please help me solve this problem: A cyclic quadrilateral has sides 5 cm, 4 cm, 7 cm, and 10 cm. Find the area of the quadrilateral. Find also the radius of the circumscribed ci      Log On


   

Question 936388: Please help me solve this problem:
A cyclic quadrilateral has sides 5 cm, 4 cm, 7 cm, and 10 cm. Find the area of the quadrilateral. Find also the radius of the circumscribed circle.
Found 2 solutions by Alan3354, AnlytcPhil:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A cyclic quadrilateral has sides 5 cm, 4 cm, 7 cm, and 10 cm. Find the area of the quadrilateral. Find also the radius of the circumscribed circle.
===============
More than 1 quadrilateral can be made with only the side lengths given.
An infinite #, actually.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!

The other tutor doesn't understand the problem.  He doesn't
know that a cyclic quadrilateral is a quadrilateral with all
four vertices lying on a circle:





We use Brahmagupta's formula to find the area of
the cyclic quadrilateral.

A=sqrt%28%28s-a%29%28s-b%29%28s-c%29%28s-d%29%29 where semiperimeter=s=%28a%2Bb%2Bc%2Bd%29%2F2,

and 

a=5, b=4, c=7, and d=10

s=%28a%2Bb%2Bc%2Bd%29%2F2=%285%2B4%2B7%2B10%29%2F2=26%2F2=13}}}



-------------

To find the radius.

Parameshvara's formula for the radius of the circumscribed circle is



We have already calculated the denominator above as 1296, so we have




Edwin