Excentre of a Triangle

Derive the formula for coordinates of excentres of a triangle?

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

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 ?

Consider the following statements : 1. The orthocentre of a triangle always lies inside the triangle. 2. The centroid of a triangle always lies inside the triangle. 3. The orthocentre of a right angled triangle lies on the triangle. 4.The centroid of a right angled triangle lies on the triangle. Which of the above statements are correct ?

Problems on Pedal Triangle and Excentre Triangle

If I_(1),I_(2),I_(3) are excentres of the triangle with vertices (0,0),(5,12),(16,12) then the orthocentre of Delta I_(1)I_(2)I_(3) is