Knowra Incircle Incircle The circle inside a triangle that is tangent to all three side segments. Its center is the triangle’s incenter, where the internal angle bisectors meet.
Incenter : The point where a triangle’s three internal angle bisectors intersect; it is equidistant from all three side lines. This point is the incircle’s center because its equal distances to the sides give the radius.
Triangle : A polygon with three sides, three vertices, and three interior angles. The incircle is defined by its position relative to a triangle’s three sides.
Triangle area : The area enclosed by a triangle, equal to half the product of a base and its perpendicular height. The incircle gives the alternative area formula: inradius multiplied by semiperimeter.
Circumcircle : The circle passing through all three vertices of a triangle, centered at the circumcenter. Unlike the incircle, it passes through the vertices rather than touching the side segments.
Angle bisector : A ray or line that divides an angle into two equal angles. The three internal angle bisectors meet at the center of the incircle.
Perpendicular distance : The shortest distance from a point to a line, measured along a perpendicular. The inradius is the same perpendicular distance from the incenter to each side.
Excircle : A circle tangent to one side of a triangle and the extensions of its other two sides. Its radius uses a related area formula, but it lies outside the triangle.
Nine-point circle : A circle through a triangle’s three side midpoints, three altitude feet, and three Euler points. It is another canonical triangle circle, but its defining points are not side tangencies.
Inradius : The radius of a triangle’s incircle, equal to the perpendicular distance from its center to any side. The inradius measures the perpendicular distance from the incenter to each tangent side.
Circle : The set of points in a plane at a fixed distance from a center. The incircle is a circle whose fixed radius reaches all three triangle sides.
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