Relationships of Circles

Introduction

This unit bundles student expectations that address properties and attributes of circles, equations of circles, and angle and segment relationships within circles. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

During this Unit

Students define new circle vocabulary, including special segments and angles of circles, using diagrams and definitions. Students use patterns, diagrams, and a variety of tools to investigate circles, chords, secants, tangents, and their angle relationships, including central and inscribed angles. Students use patterns, diagrams, and a variety of tools to investigate circles, chords, secants, tangents, and their segment length relationships. Students apply theorems about combined circle angle/segment length relationships, including central and inscribed angles, in non-contextual problems. Students describe and develop the concept of radian measure of an angle as the ratio of the length of an arc intercepted by a central angle and the radius of the circle. Students convert between degree and radian measures. Students develop the equation of a circle, x² + y² = r², using the coordinate grid and the Pythagorean Theorem, given the radius, r, and center at the origin. Students determine the equation of a circle, (x – h)² + (y – k)² = r², given the radius and a center of (h, k). Students represent real-world situations using equations of circles.