Question

Let the orthocenter and centroid of a triangle be a(-3, 5) ,b(3, 3) respectively. If c is the circumcenter of this triangle, then the radius of the circle having line segment ac as diameter, is

Answer 1

Answer:

Radius is $\frac{3\sqrt10}{2}units$

Step-by-step explanation:

By Section formula

$\frac{2h+(-3)}{3}=3$    ,   $\frac{2k+5}{3}=3$

⇒ 2h-3=9                                 ,   ⇒ 2k+5=9

⇒ h=6                                          ⇒ k=2

The point C is (6,2)

AC is diameter and the coordinates of point A is (-3,5)

$AC=\sqrt(9^2+3^2)=3\sqrt(9+1)=3\sqrt10$

Hence, radius is $\frac{3\sqrt10}{2}units$

Answer 2

Refer to the attachment above for your answer!!...✔✔