Question

the vertices of a triangle are (5,1),(11,1)And(11,9­).find the co-ordinates of the circumcemtre of the triangle.

Answer 1

 Vertices of the triangle are A(5,1), B(11,1) and C (11,9).

 

Let P(x, y) be the circumcenter of the triangle.

 

So, PA = PB = PC  (Circumcenter is equidistant from the vertices of the triangle)
=>(PA)2 = (PB)2

=>{(x – 5)2 + (y – 1)2} = {(x –11)2 + (y - 1)2}

=>x2 + 25 – 10x + y2 + 1 – 2y = x2 + 121 – 22x + y2 + 1 - 2y
=> 12x = 96
=> x = 8.........(1)
 

 

As,(PA)2 = (PC)2

=>{ (x –5)2 + (y – 1)2 } = { (x – 11)2 + (y - 9)2 }

=> x2 + 25 – 10x + y2 +1 –2y = x2 + 121 – 22x + y2 + 81 - 18y

=> 25+1 -10x-2y = 121+81-22x -18y
=> 26-10x-2y= 202 -22x-18y
=> 22x-10x +18y-2y = 202 -26
=> 12x +16y = 276
=> 12(8) +16y = 276 .....(using 1)
=> 16y = 276-96
=> 16y = 180
=> y = 180/16
=>y = 45/4 

Answer 2

Step-by-step explanation:

I hope this may help you