Orthocentre and centroid of a triangle are A(−3,5) and B(3,3) respectively. If C is the
circumcentre and AC is the diameter of this circle, then find the radius of the circle
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Answer:
(centroid ) divides orthocentre and circumcentre in ratio 2:1
Lets circumcentre be (c)=(x,y)
(3,3);B=
3
2(x)+1+(−3)
,
3
2(y)+1(5)
2x−3=9⇒x=6
2y+5=9⇒y=2
Circumcentre will be (6,2)
AC is a diameter .
A(−3,5) C(6,2)
AC=
9
2
+3
2
=
90
Radius =
2
AC
=
2
90
=
7
90
2
45
=
2
3
5
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