PlanimetricsCalculationContext

Constructs centroid of triangle ABC.

Constructs circle (as Quadric) by its center and point on it.

Constructs circle (as Quadric) by the given opposite points on it.

Constructs circumcenter of triangle ABC.

Constructs circumcircle of triangle ABC as Quadric.

Returns an expression which equality to zero is equivalent to collinearity of the points.

Tests if the points are collinear.

Returns an expression which equality to zero is equivalent to concurrency of the lines.

Tests if the lines are

Constructs a point P on the line through A and B that divides segment \( AB \) in ratio lambda. It means that on the affine map that is considered generated by Point.x and Point.y coordinates a point P such that \(\overrightarrow{AP}/\overrightarrow{PB} = \lambda\), so P is returned.

Constructs a point P on the line through A and B that divides segment \( AB \) in ratio \(a/b\). It means that on the affine map that is considered generated by Point.x and Point.y coordinates a point P such that \(\overrightarrow{AP}/\overrightarrow{PB} = a/b\), so P is returned.

Constructs Euler's circle of triangle ABC as Quadric.

Constructs Euler line of triangle ABC.

Constructs intersection of the given lines l and m.

Checks if the given quadric is circle.

Checks if this point is lying on the line l.

Checks if this point is lying on the quadric q.

Checks if this line is lying through the point P.

Checks if this quadric is lying through the point P.

Checks if this point is not lying on the line l.

Checks if this point is not lying on the quadric q.

Checks if this line is not lying through the point P.

Checks if this quadric is not lying through the point P.

Checks if this line is not tangent to the quadric q.

Checks if this quadric is not tangent to the line l.

Checks if this line is tangent to the quadric q.

Checks if this quadric is tangent to the line l.

Constructs line that goes through the given points A and B.

Returns an expression which equality to zero is equivalent to condition of P lying on l.

Returns an expression which equality to zero is equivalent to condition of P lying on q.

Constructs a midpoint between A and B. The affine map is considered generated by Point.x and Point.y coordinates.

Constructs orthocenter of triangle ABC.

Constructs perpendicular in terms of affine map that is considered generated by Point.x and Point.y coordinates line to the given line l through the given point A.

Construct a normal projection in terms of affine map that is considered generated by Point.x and Point.y coordinates of this point to the given line l.

See also: wiki

Returns an expression which equality to zero is equivalent to condition of l being tangent to q.