x The vertices of
triangle
are A (a,0), Blo,b) and
c(a,b) then the circumscentre is
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Answer:
The given vertices represent a right angled triangle with right angle at C(a,b) and the hypotenuse AB, as AB
2
=AC
2
+BC
2
So that orthocentre of the triangle is at C(a,b).
Circumcentre of the triangle is the middle point of the hypotenuse AB i.e. (a/2,b/2)
And centroid of the triangle is
(
3
a+a+0
,
3
0+b+b
)=(
3
2a
,
3
2b
)
Let P(x,y) be the foot of the altitude from C.
Then P lies on AB whose equation is
a
x
+
b
y
=1 ( 1 )
Also CP is perpendicular to AB and its equation
⇒y−b=(a/b)(x−a) ( 2 )
Solving (1) & (2) we get
x=
a
2
+b
2
a
3
,y=
a
2
+b
2
b
3
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