Generator
circle-angle
A generator in the geometry library, called 7 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.
circle-angle is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "same"
show: "proof"
show: "thales"
show: "cyclic"
What it checks while it draws
Collected by running the family and listening to lib/verify.js, not written
here. The count is how many separate times this build put that claim to the test.
- A lies on the circle ×1
- and so do the other two ×1
- and the same on the other side ×1
- B lies on the circle ×1
- every apex on the arc gives the same angle ×1
- one angle, not several ×1
- opposite angles add to a straight angle ×1
- the angle on a diameter is a right angle ×1
- the apex is on the major arc ×1
- the apex lies on the circle ×1
- the centre's angle is twice the apex's ×1
- the chord is a diameter ×1
- the exterior angle is twice the base angle ×1
- the quadrilateral's angles add to 360° ×1
- the two halves are the whole angle ×1
- triangle OPA is isosceles ×1
- triangle OPB is isosceles ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.