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ABC Fig ABCD altitude bisects Brocard points center of inversion centroid Ceva's Theorem Cevians chord circle of inversion circle orthogonal circumcenter circumcircle circumradius coaxal system concurrent Construct a circle construct the triangle corresponding sides cuts cyclic quadrilateral determined diameter distance equation excircle external geometry given angle given circles given elements given line given point given ratio given triangle harmonic range Hence homothetic center homothetic ratio inscribed inverse points isogonal conjugate isosceles line joining line of centers line segment locus median mid-point nine-point circle opposite angle opposite side orthic triangle orthocenter orthocentric group pairs parallel pedal triangle perpendicular bisector points of intersection points with respect polar polygon problem proof properties Prove radical axis radii radius required circle required triangle right triangle secant Show similar triangles Simson line solution square subtends symmedian point system of circles tangent Theorem 13 triangle ABC vertex vertices