Evidence of Understanding

**investigate and describe the relationships that exist between the segments on a circle**- investigate and describe how the lengths of segments for two intersecting
**chords**, two**secants**(drawn from the same point), or a**tangent**and a secant (drawn from the same point) are related- prove theorems about the segments of secants, tangents, or intersecting chords

- recognize congruent chords are equidistant from the center of the circle
- recognize tangents from a shared point outside the circle are congruent
- calculate the length of an unknown segment

- investigate and describe how the lengths of segments for two intersecting
**analyze and apply characteristics of polygons that circumscribe or are inscribed in a circle**- use constructions to visualize the congruent relationships when
**inscribing**or**circumscribing**a polygon in the circle- construct an equilateral triangle, square or regular hexagon inscribed in a circle
- construct a right triangle inscribed in a circle using perpendicular bisectors
- construct a circle that is inscribed in a triangle using angle bisectors

- use constructions to identify and define the
**incenter**of a triangle - prove properties of angles for a quadrilateral inscribed in a circle
*Example: quadrilaterals inscribed in a circle have opposite angles that are supplementary*

- find the missing value of an unknown angle or segment involving a polygon and a circle

- use constructions to visualize the congruent relationships when
**use circles in modeling situations and find missing values**- create diagrams that can be used to represent the situation
- use markings and notations to create equations that can be used to find missing values

Develop conceptual understanding:

chord, secant, tangent, secants, inscribed, circumscribed, incenter

Supporting terms to communicate:

radius, equivalent, ratio, proportion, similarity, scale factor, dilation, right triangle, equilateral, regular polygon, quadrilateral, perpendicular, bisect, intersect, intercepted arc, supplementary