Determining the missing lengths and angles of a triangle + triangle centers (kimberling numbers)
With this tool you can determine the missing lengths and angles of a triangle as well as determine some important triangle centers.
It takes 3 out of the 6 input fields (3 sides, 3 corners) to solve a triangle.
If you enter less or more than 3 input fields, the result is not reliable.
That is to say, either you enter 3 sides, or 3 corners, or 2 sides and 1 corner, or 1 side and 2 corners.
Because there are an infinite number of triangles as a solution that meet 3 given angles, the length of 1000 mm is presupposed.
After pressing the calculate! button a check is performed if the input values are valid.
When entering 3 angles, the sum of the three angles must be equal to 180 degrees.
When entering 3 lengths, the sum of each 2 lengths must be greater than the third length.
If 1 of the two conditions is not met, an error message appears in red in a comment field.
With a valid entry, you will receive a graphical result in addition to the calculation results.
The graphic result includes the drawing of the triangle to scale, the location of the incentre of the inscribed circle
(X1), the position of the centroid (centre of gravity) (X2), the position of the circumcenter and the
defined circle passing through the three vertices of the triangle (X3), the orthocenter of the triangle (X4), the position of
the nine-point centre of the nine-point circle (X5) and the location of the point of Gergonne (X7).
With the “total survey” selection box, you can choose between maximum visibility of the triangle regardless of the size
of the circumscribed circle and location of the orthocenter or a total overview where the circumscribed circle falls
within the canvas.
Select the ellipse correction box and press calculate again if the ellipse does not pass through the 3 vertices or if
the ellipse results deviate too much from value 1. If this does not help approach the angle: for example in stead of 90, enter 89.999.
| Length a | 0 | mm | ||
| Length b | 0 | mm | ||
| Length c | 0 | mm | ||
| Angle alfa | 0 | degrees | 0 | radians |
| Angle beta | 0 | degrees | 0 | radians |
| Angle gamma | 0 | degrees | 0 | radians |
| Total angle alfa+beta+gamma | 0 | degrees | 0 | radians |
| Circumference of the triangle a+b+c | 0 | mm | ||
| Half circumference of the triangle | 0 | mm | ||
| Area of the triangle | 0 | mm2 | ||
| Area of the triangle according Heron | 0 | mm2 | ||
| Area of the inscribed Steiner ellipse | 0 | mm2 | ||
| Area of the circumscribed Steiner ellipse | 0 | mm2 | ||
| Length median from point 3 on a | 0 | mm | ||
| Length median from point 1 on b | 0 | mm | ||
| Length median from point 2 on c | 0 | mm | ||
| Length perpendicular from point 3 on a | 0 | mm | ||
| Length perpendicular from point 1 on b | 0 | mm | ||
| Length perpendicular from point 2 on c | 0 | mm | ||
| Eq. of straight through point 1 and 2 | 0 | |||
| Eq. of straight through point 2 and 3 | 0 | |||
| Eq. of straight through point 1 and 3 | 0 | |||
| Eq. straight through point 3 perp. to a | 0 | |||
| Eq. straight through point 1 perp. to b | 0 | |||
| Eq. straight through point 2 perp. to c | 0 | |||
| Eq. median through point 1 | 0 | |||
| Eq. median through point 2 | 0 | |||
| Eq. median through point 3 | 0 | |||
| Eq. perpendicular in the middle of a | 0 | |||
| Eq. perpendicular in the middle of b | 0 | |||
| Eq. perpendicular in the middle of c | 0 | |||
| Eq. bisector through point 1 | 0 | |||
| Eq. bisector through point 2 | 0 | |||
| Eq. bisector through point 3 | 0 | |||
| Point 1 x coordinate | 0 | Point 1 y coordinate | 0 |
| Point 2 x coordinate | 0 | Point 2 y coordinate | 0 |
| Point 3 x coordinate | 0 | Point 3 y coordinate | 0 |
| X1 = Intersection bisectors: x coordinate | 0 | X1 = Intersection bisectors: y coordinate | 0 |
| Radius inscribed circle | 0 | Diameter inscribed circle | 0 |
| X2 = centroid x coordinate | 0 | X2 = centroid y coordinate | 0 |
| X3 = circumcenter x coordinate | 0 | X3 = circumcenter y coordinate | 0 |
| Radius circumscribed circle | 0 | Diameter circumscribed circle | 0 |
| X4 = Orthocenter x coordinate | 0 | X4 = Orthocenter y coordinate | 0 |
| X5 = Nine-point center x | 0 | X5 = Nine-point center y | 0 |
| Radius nine-point circle | 0 | Diameter nine-point circle | 0 |
| Semi major axis a of the Steiner ellipse | 0 | Semi minor axis b of the Steiner ellipse | 0 |
| Ellipse result 1 | 0 | Ellipse result 2 | 0 |
| Rotation ellipse (radians) | 0 | Rotation ellipse (degrees) | 0 |
| Rotation ellipse simplified (radians) | 0 | Rotation ellipse simplified (degrees) | 0 |
| Applied scale factor | 0 |
The blue dashed line is the Euler line.
This line connects orthocenter, nine-point center, centroid and circumcenter.
Tangents of the inscribed circle with the 3 triangle sides
| x coord tangent to a | 0 | y coord tangent to a | 0 |
| x coord tangent to b | 0 | y coord tangent to b | 0 |
| x coord tangent to c | 0 | y coord tangent to c | 0 |
| rico 1 (through pt 3, tangent to a) | 0 | bterm 1 (through pt 3, tangent to a) | 0 |
| rico 2 (through pt 1, tangent to b) | 0 | bterm 2 (through pt 1, tangent to b) | 0 |
| rico 3 (through pt 2, tangent to c) | 0 | bterm 3 (through pt 2, tangent to c) | 0 |
| X7 = Gergonne intersection x coordinate | 0 | X7 = Gergonne intersection y coordinate | 0 |