AMSCO'S Geometry. New York - Rye High School

560 Geometry of the CircleIn the diagram, CD gis tangent to circleP at C and to circle P at D. TangentCD gis said to be a common external PPtangent because the tangent does not Cintersect the line segment joining the centersof the circles.DThe diagrams below show that two circles can have four, three, two, one, orno common tangents.4 commontangents3 commontangents2 commontangents1 commontangentNo commontangentsTwo circles are said to be tangent to each other if they are tangent to thesame line at the same point. In the diagram, ST gis tangent to circle O and tocircle O at T. Circles O and O are tangent externally because every point ofone of the circles, except the point of tangency, is an external point of the othercircle.O T O In the diagram,gis tangent to circle P andto circle P at M. Circles P and P are tangentS internally because every point of one of the circles,except the point of tangency, is an internalMPpoint of the other circle.PEXAMPLE 1Given: Circles O and O with a common internaltangent, , tangent to circle O at A andcircle O at B, and C the intersection of OOrand AB g.Prove: ACBC 5 OCOrCAB g MNOACBNO