Question

Find the co-ordinates of the circum centre of the triangle whose vertices are P(5, 1), ((-3,-7)
R(7,-1). Also find the area of the circle.​

Answer 1

Step-by-step explanation:

Let the co-ordinate of the circumcentre be (a,b) and let it be O.

WE KNOW THAT,

BY USING DISTANCE FORMULA, WE CAN FIND IT.

OP²=OQ²=OR²

(a-5)² + (b-1)²= (a+3)² + (b+7)²= (a-7)² + (b+1)²

IN THE FIRST WE TAKE,

OP²=OQ²

(a-5)² + (b-1)²= (a+3)² + (b+7)²

a²+25-10a+b²+1-2b=a²+9+6a+b²+49+14b

-32=16a+16b

-2=a+b

a=-2-b------(1)

IN SECOND WE TAKE,

OQ²=OR²

(a+3)² + (b+7)²= (a-7)² + (b+1)²

a²+9+6a+b²+49+14b=a²+49-14a+b²+1+2b

8= -20a- 12b

5a+3b=-2---------(2)

from 1st and second equation

5(-2-b) + 3b=-2

-10-5b+3b =-2

-2b= 8

b=-4

AND

a=2

the co-ordinate of circumcentre is (2,-4).

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