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Circles in contact

Circles can either touch other circles or lines, which we call tangents. When two or more circles touch, we add or subtract their radi construct their special point of tangencies. When circles touch tangents, we have special constructions as well to use so that we find the exact point of tangency. A point of tangency is always perpendicular to the circle. A line from the point of tangency to the centre of the circle produces a normal. Normals and tangents are also perpendiculat to each other.

drawing a tangent from a point to a circle tangents to equal circles tangents to unequal circles