Valerie Russell

Assignment 7

Construct a circle tangent to two other circles.

Examples of Tangent Circles

Two circles are said to be tangent circles if their intersection consists of exactly one point. Imagine a line that touches the two circles where the circles intersect. This line would be the tangent line. If circles are on opposite sides of a tangent line, the circles are said to be externally tangent. If the circles are on the same side of the tangent line, they are said to be internally tangent.

Another Construction

A GSP Construction

To construct a circle tangent to two other circles you must first construct circle A using radius AB. Choose any two points inside circle A ( x and y) and construct another circle with center X. Now choose a point on circle A(call it C) and construct a line through AC. Construct circle C with a radius the same radius as XY. Name the point D where line AC intersects circle C. Constuct segment XD and its perpendicular bisector. Label the intersection O. Construct circle Z tangent to circle A and X using radius ZC. using GSP you can rotate point C.

 The idea of this construction is to construct a circle Z tangent to both circles A and X. The key is to construct a circle that lies on the diameter of circle C and circle A.To see the animation and a list of instructions please See script tool.

Two circles are said to be tangent circles if their intersection consists of exactly one point.