Find the coordinates of the circumcenter of the triangle
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find the coordinates of the circumcentre of the triangle whose vertices (8,6) , (8,-2) & (2,-2). also find the circumradius.
Answered by admin @
To Find :- The circum - radius.
Let, A ( 8,6 ) , B ( 8,-2 ) and C ( 2,-2 ) be the vertices of the given triangle.
And also let P ( x,y ) be the circumcenter of this triangle.
PA = PB = PC
PA² = PB² = PC²
Now, PA² = PB²
( x-8 )² + ( y-6 )² = ( x-8 )² + ( y+2 )²
x² + y² - 16x - 12y + 100 = x² + y² - 16x + 4y + 68
16y = 32
y = 2
And
PB² = PC²
( x - 8 )² + ( y + 2 )² = ( x - 2 )² + ( y + 2 )²
x² + y² - 16x + 4y + 68 = x² + y² - 4x + 4y + 8
12x = 60
x = 5
So, the coordinates of the circumcentre P are ( 5,2 )
Also Circum-radius = PA = PB = PC = √(5-8)² + (2-6)²
⇒ 5.
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