A triangle has corners at $(8 ,7 )$ , $(2 ,1 )$ , and $(5 ,6 )$ . What is the area of the triangle's circumscribed circle?

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A triangle has corners at $(8 ,7 )$ , $(2 ,1 )$ , and $(5 ,6 )$ . What is the area of the triangle's circumscribed circle?

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Answer 1 · 2017-07-12T11:46:55

The area of the circle is $=133.5u^2$

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,

$(8-a)^2+(7-b)^2=r^2$ ....... $(1)$

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

$(5-a)^2+(6-b)^2=r^2$ ......... $(3)$

We have $3$ equations with $3$ unknowns

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

$64-16a+a^2+49-14b+b^2=4-4a+a^2+1-2b+b^2$

$12a+12b=108$

$a+b=9$ ............. $(4)$

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

$4-4a+a^2+1-2b+b^2=25-10a+a^2+36-12b+b^2$

$6a+10b=56$

$3a+5b=28$ .............. $(5)$

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

$3(9-b)+5b=28$

$27-3b+5b=28$

$2b=1$ , $=>$ , $b=1/2$

$a=9-1/2$ , $=>$ , $a=17/2$

The center of the circle is $=(17/2,1/2)$

$r^2=(2-17/2)^2+(1-1/2)^2=(-13/2)^2+(1/2)^2$

$=170/4$

$=85/2$

The area of the circle is

$A=pi*r^2=pi*85/2=133.5$

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A triangle has corners at $(8 ,7 )$ , $(2 ,1 )$ , and $(5 ,6 )$ . 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 (8 ,7 )(8 ,7 ), (2 ,1 )(2 ,1 ), and (5 ,6 )(5 ,6 ). What is the area of the triangle's circumscribed circle?

1 Answer

Explanation:

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A triangle has corners at $(8 ,7 )$ , $(2 ,1 )$ , and $(5 ,6 )$ . What is the area of the triangle's circumscribed circle?