Differential Equations

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

$\frac{3 \sqrt{5}}{2}$

$\sqrt{10}$

$2 \sqrt{10}$

$3 \sqrt{\frac{5}{2}}$

Solution

$3 \sqrt{\frac{5}{2}}$

A(-3,5)

B(3,3)

so,

$A B = \sqrt[2]{10} N o w, a s, A C = \frac{3}{2} A B S o, R a d i u s = \frac{3}{4} A B = \frac{3}{2} \sqrt{10} = 3 \sqrt{\frac{5}{2}}$