**ERIC Number:**EJ875491

**Record Type:**Journal

**Publication Date:**2006

**Pages:**12

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

The Radical Axis: A Motion Study

McGivney, Ray; McKim, Jim

AMATYC Review, v27 n2 p3-14 Spr 2006

Interesting problems sometimes have surprising sources. In this paper we take an innocent looking problem from a calculus book and rediscover the radical axis of classical geometry. For intersecting circles the radical axis is the line through the two points of intersection. For nonintersecting, nonconcentric circles, the radical axis still exists. We are interested in the relationship of this line to the two circles in this latter case. We take an algebraic approach to its formula so we can see this relationship as we move and scale the defining circles. This approach culminates in the discovery that if the two circles grow so that their areas increase at equal rates then the radical axis remains constant and in fact is the eventual line of intersection of the two circles.

Descriptors: Geometry, Calculus, Mathematics Instruction, College Mathematics, Community Colleges, Geometric Concepts, Problem Solving, Algebra, Mathematical Formulas

American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org

**Publication Type:**Journal Articles; Reports - Evaluative

**Education Level:**Postsecondary Education; Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A