Question

A, B, C are vertices of a triangle with right angle at A and P(-4, 0); Q(0, 6) are two given points. If the ratio of distances from each vertex to P, to that of Q is 2 : 3, then the centroid of $\triangle$ABC lies on a circle with radius equal to

• A. $\frac{4\sqrt{13}}{5}$ units
• B. 4 units
• C. $\frac{8\sqrt{13}}{5}$ units
• D. 8 units

Answer 1

Answer: (A)

$\frac{4\sqrt{13}}{5}$ units

Answer 2

The vertices lie on the Apollonius circle. The centroid $G=(A+2O)/3$ thus traces a circle with center $O$ and radius $R/3=\frac{4\sqrt{13}}{5}$.