circles

  • A CIRCLE is a perpendicular relationship between two points

In other words, A CIRCLE is a rotation of one point about the other.

Lines are "straight-forward" to consider. Circles just take you around and around.

like lines, circles are instantiated with twp points Unlike lines, the two points are not interchangeable one is defined and the center point, the other as the radius point

we use these points to derive the equation

  • (x - h)^2 + (y - k)^2 + r^2 = 0

// x offest
this.h = centerPoint.x;

// y offset
this.k = centerPoint.y;

//get radius length
this.r = centerPoint.distanceTo(radiusPoint);

// generate equation for circle
// (x - h)^2 + (y - k)^2 + r^2
this.eq = Algebrite.run( `clearall
  (x - (${this.h}))^2 + (y - (${this.k}))^2 - (${this.r})^2` );
// log("   eq: " + this.eq);

right now - the circle does not have the equivalent of a xRoot or yRoot expression in the object this work is done in the intersection calculation

fairly straightforward until we get to the intersections

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