Find the coordinates of the cicumcentre of the triangle whose vertices are (8,6), (8,-2) and (2,-2). Also find its circumradius.

(plz explain step wise)

Hi!
Here is the answer to your question.
 
 
Vertices of the triangle are A(8, 6), B(8, –2) and C (2, –2).
 
Let P(x, y) be the circumcenter of the triangle.
 
So, PA = PB = PC   (Circumcenter is equidistant from the vertices of the triangle)
 
Cheers!

  • 109

 First find the midpoints of the  any two sides. Also find the equations of those sides .Then find the equatios of  lines passing through those midpoints and perpendicular to the respective sides. The point of intersection of those two perpendicular lines will be the circumcentre. The distance of the circumcentre .from any vertex will be the  circumradius .

Hope this will help you.

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Hi Maryam !!!!!

Circumcentre is the point in the circle which is equidistant from vertices of the triangle .....

Let the circumcentre = P(x,y) ...... A = (8,6) ...... B = (8,-2) ..... C = (2,-2) .....

As , PA = PB

----> {√(x – 8)2  + (y – 6)2} = {(√x – 8)2 + (y + 2)2}

------>  x2 + 64 – 16x + y2 + 36 – 12y  =  x2 + 64 – 16x + y2 + 4 + 4y

------> 16y = 32

------>  y = 2 ….

As, PA = PC

----> { √(x – 8)2  + (y – 6)2 } = { (√x – 2)2 + (y + 2)2 }

---->  x2 + 64 – 16x + y2 + 36 – 12y  =  x2 + 4 – 4x + y2 + 4 + 4y

----> 100 – 16x – 12y = 8 – 4x + 4y

----> 100 – 16x – 24 = 8 – 4x + 8

----> 76 – 16x = 16 – 4x

---->  60 = 12x

----> x = 5

So, Circumcentre = P(2,5) ..........

Hope this helps !!!!!

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 Circum centre will be ( 5 , 2 ) .

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really sorry for the mistype !!!!!

So, The circumcentre = P(x,y) = (5,2) ......

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