Excentre of a Triangle

Derive the formula for coordinates of excentres of a triangle?

The circumcentre of a triangle lies with in the triangle only when the triangle is

If the circumcentre of a triangle lies outside the triangle then the triangle is

If circumcentre of a triangle is outside the triangle, then what is the type of triangle?

Incentre of a triangle lies in the interior of: (A) an isosceles triangle only (B) a right angled triangle only (C) any equilateral triangle only (D) any triangle

If the circumcentre of a triangle lies outside the triangle, then what type of triangle is it ?

In which type of triangle does the circumcentre of a triangle lie in the exterior of the triangle?

The excentre of the triangle formed by the points (0, 3), (4, 0), (0, 0) which is opposite to (0, 0) is

In a triangle ABC I_1, I_2,I_3 are excentre of triangle then show that II_(1). II_(2). II_(3)=16R^(2)r.