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Question

Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is:

Options

A.

210

B.

352

C.

352

D.

10

Solution

Orthocentre A(-3, 5) centroid B(3, 3) and AB
=40=210

Centroid divides orthocentre and circumcentre in ratio 2 :1
∴ AB : BC = 2 : 1
Now AB = 23 AC
AC = 32. AB = 32(210)
AC = 310
Radius of circle with AC as diametre is
3210=352

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