Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the cir

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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:

Accepted Answer

Orthocentre A(-3, 5) centroid B(3, 3) and AB
$= \sqrt{40} = 2 \sqrt{10}$

Centroid divides orthocentre and circumcentre in ratio 2 :1
$∴$ AB : BC = 2 : 1
Now AB = $\frac{2}{3}$ AC
AC = $\frac{3}{2}$ . AB = $\frac{3}{2}$ $(2 \sqrt{10})$
AC = $3 \sqrt{10}$
Radius of circle with AC as diametre is
$\frac{3}{2} \sqrt{10} = 3 \sqrt{\frac{5}{2}}$

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