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Triangle Defined by 3 Points

X1 Y1
X2 Y2
X3 Y3
     
   
Area
Perimeter
Intersection point (x,y) of the medians:
Intersection point (x,y) of the altitudes:
Incircle radius:
Circumcircle radius:
intersection point of the angles bisector (incircle center)
intersection point of the sides perpendicular bisectors (circumcircle center):
Side 1 - 2 Side 1 - 3 Side 2 - 3
Angle   α Angle   β Angle   γ
Altitude h1 Altitude h2 Altitude h3
Median m1 Median m2 Median m3

Equations of a triangle defined by 3 points

Print triangle defined by 3 points
Triangle given by 3 points
(x1 , y1), (x2 , y2) and (x3 , y3)
Triangle definition
The area is given by:
Triangle area
Triangle area
Perimeter (P)
Triangle perimeter
Triangle angles:
Triangle angles
We have to remember that if the result of the angle is negative then we have to translate it into a positive angle by the formula:    
angle = 2 · pi   angle.
Intersection point of the medians. Triangle definition Intersection point of the medians (x , y)
(centroid - also known as the center of gravity).

Intersection of medians
The lengths of the medians are:
Intersection of medians
Intersection point of the triangle altitudes (orthocentre)
Triangle definition
Intersection of altitudes
After solving the determinants x and y will be:
x coordinate of the triangle altitudes intersection
y coordinate of the triangle altitudes intersection
The lengths of the altitudes are found by the formulas:
y coordinate of the triangle altitudes intersection
Intersection point of the sides perpendicular bisectors (circumcircle)
Triangle definition sides perpendicular bisectors intersection
After solving the determinants, we get the x and y coordinates:
x coordinate of sides perpendicular bisectors intersection
y coordinate of sides perpendicular bisectors intersection
The circumcircle radius can be found by calculating the distance of the center point (x , y) from any one of the triangle vertices:
Incircle radius
Intersection point (x , y) of the angles bisectors (incircle)
Triangle angle bisector definition
 We denote a, b and c as the lengths of the triangle sides.
Angles bisectors coordinate
The incircle radius can be found by calculating the distance of the center point (x , y) from one of the sides of the triangle:
Incircle radius