Question

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​

Answer 1

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