Related: Is this quadrilateral cyclic?
Background
A tangential quadrilateral is a quadrilateral which has an incircle:
Examples include any square, rhombus, or a kite-like shape. Rectangles or parallelograms in general are not tangential.
Task
Given the four vertices of a quadrilateral (as Cartesian coordinates), determine if it is tangential.
Input & output
For input, it is allowed to use any format that unambiguously specifies the four vertices' coordinates (eight real or floating-point numbers). You can assume the following on the input:
- The points specify a simple convex quadrilateral, i.e. all internal angles are strictly less than 180 degrees, and the edges meet only at the vertices.
- The points are specified in counter-clockwise order (or the other way around if you want).
For output, you can use one of the following:
- Truthy/falsy values as defined by your language of choice (swapping the two is allowed), or
- Two consistent values for true/false respectively.
It is acceptable if your code produces wrong output due to floating-point inaccuracies.
Test cases
Tangential
(0, 0), (0, 1), (1, 1), (1, 0) # unit square
(-2, 0), (0, 1), (2, 0), (0, -1) # rhombus
(1, -2), (-2, -1), (-1, 2), (4, 2) # kite
(0, 0), (50, 120), (50, 0), (32, -24) # all four sides different
Not tangential
(0, 0), (0, 1), (2, 1), (2, 0) # rectangle
(0, 0), (1, 1), (3, 1), (2, 0) # parallelogram
Scoring & winning criterion
Standard code-golf rules apply. The shortest code in bytes wins.