This is a collection of 110 (in binary) 2D geometry problems. CircumscribedCircle x1 y1 x2 y2 x3 y3 Find out the circumscribed circle of triangle (x1,y1)-(x2,y2)-(x3,y3). These three points are guaran
This is a collection of 110 (in binary) 2D geometry problems. CircumscribedCircle x1 y1 x2 y2 x3 y3 Find out the circumscribed circle of triangle (x1,y1)-(x2,y2)-(x3,y3). These three points are guaranteed to be non-collinear. The circle is formatted as (x,y,r) where (x,y) is the center of circle, r is the radius. InscribedCircle x1 y1 x2 y2 x3 y3 Find out the inscribed circle of triangle (x1,y1)-(x2,y2)-(x3,y3). These three points are guaranteed to be non-collinear. The circle is formatted as (x,y,r) where (x,y) is the center of circle, r is the radius. TangentLineThroughPoint xc yc r xp yp Find out the list of tangent lines of circle centered (xc,yc) with radius r that pass through point (xp,yp). Each tangent line is formatted as a single real number “angle” (in degrees), the angle of the line (0<=angle<180). Note that the answer should be formatted as a list (see below for details). If there is no answer, you should print an empty list. CircleThroughAPointAndTangentToALineWithRadius xp yp x1 y1 x2 y2 r Find out the list of circles passing through point (xp, yp) that is tangent to a line (x1,y1)-(x2,y2) with radius r. Each circle is formatted as (x,y), since the radius is already given. Note that the answer should be formatted as a list. If there is no answer, you should print an empty list. CircleTangentToTwoLinesWithRadius x1 y1 x2 y2 x3 y3 x4 y4 r Find out the list of circles tangent to two non-parallel lines (x1,y1)-(x2,y2) and (x3,y3)-(x4,y4), having radius r. Each circle is formatted as (x,y), since the radius is already given. Note that the answer should be formatted as a list. If there is no answer, you should print an empty list. CircleTangentToTwoDisjointCirclesWithRadius x1 y1 r1 x2 y2 r2 r Find out the list of circles externally tangent to two disjoint circles (x1,y1,r1) and (x2,y2,r2), having radius r. By “externally” we mean it should not enclose the two given circles. Each circle is formatted as (x,y), since the radius is already given. Note that the answer should be formatted as a list. If there is no answer, you should print an empty list. For each line described above, the two endpoints will not be equal. When formatting a list of real numbers, the numbers should be sorted in increasing order; when formatting a list of (x,y) pairs, the pairs should be sorted in increasing order of x. In case of tie, smaller y comes first.
