A triangle has corners at $(9 ,4 )$ , $(7 ,1 )$ , and $(3 ,6 )$ . What is the area of the triangle's circumscribed circle?

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A triangle has corners at $(9 ,4 )$ , $(7 ,1 )$ , and $(3 ,6 )$ . What is the area of the triangle's circumscribed circle?

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Answer 1 · 2017-06-13T07:36:44

The area of the circumscribed circle is $=34.6u^2$

Explanation:

To calculate the area of the circle, we must calculate the radius $r$ of the circle

Let the center of the circle be $O=(a,b)$

Then,

$(9-a)^2+(4-b)^2=r^2$ ....... $(1)$

$(7-a)^2+(1-b)^2=r^2$ .......... $(2)$

$(3-a)^2+(6-b)^2=r^2$ ......... $(3)$

We have $3$ equations with $3$ unknowns

From $(1)$ and $(2)$ , we get

$81-18a+a^2+16-8b+b^2=49-14a+a^2+1-2b+b^2$

$4a+6b=47$

$4a+6b=47$ ............. $(4)$

From $(2)$ and $(3)$ , we get

$49-14a+a^2+1-2b+b^2=9-6a+a^2+36-12b+b^2$

$8a-10b=5$

$8a-10b=5$ .............. $(5)$

From equations $(4)$ and $(5)$ , we get

$94-12b=5+10b$

$22b=89$

$b=89/22$

$4a=47-6*89/22=47-3*89/11=250/11$ , $=>$ , $a=250/44=125/22$

The center of the circle is $=(125/22,89/22)$

$r^2=(3-125/22)^2+(6-89/22)^2=(59/22)^2+(43/22)^2$

$=5330/484$

$=2665/242$

The area of the circle is

$A=pi*r^2=2665/242*pi=34.6$

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A triangle has corners at $(9 ,4 )$ , $(7 ,1 )$ , and $(3 ,6 )$ . What is the area of the triangle's circumscribed circle?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

A triangle has corners at (9 ,4 )(9 ,4 ), (7 ,1 )(7 ,1 ), and (3 ,6 )(3 ,6 ). What is the area of the triangle's circumscribed circle?

1 Answer

Explanation:

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A triangle has corners at $(9 ,4 )$ , $(7 ,1 )$ , and $(3 ,6 )$ . What is the area of the triangle's circumscribed circle?