Find Equation of Circle Inscribed in a Triangle Formed by Intersection of Three Lines

Circumcenter of a triangle is the point of intersection of the right bisector of the three sides of a triangle. All the three vertices are same distance away from the circumcentre and so a circle can be drawn circumscribing the triangle using this point as the centre. Orthocentre of a triangle is a point where the perpendiculars drawn from each vertex to the opposite sides intersect. For an acute angle triangle, the orthocenter is inside the triangle; for right triangle it is on the hypotenuse and for the obtuse angle triangle it lies outside the triangle. Incentre of a triangle is the point of intersection of three interior angles of a triangle. A circle inscribed in a triangle can be drawn with center at the incenter.
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