Question

The diameter of the nine point circle of the triangle with vertices $(3,4),\left(5\cos \theta ,5\sin \theta \right)$ and $(5\cos \theta ,-5\sin \theta )$, where $\theta \in R$, is

• A. $10$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is A $10$

$(3,4),(5\cos \theta ,5\sin \theta ),(5\cos \theta ,-5\sin \theta )$

The vehicles of triangle lies on the line eqn

$x^2+y^2=25=r^2$

here radius is $5units$ & centre at origin circumcentre is the origin of centroid is

$(\frac{5\sin \theta +5\cos \theta +3}{3},\frac{5\sin \theta -5\cos \theta +4}{3})$

Radius is $5units$

& so diameter, $d=2r=10units$