Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Circles
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand and apply theorems about circles. (Geometry - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes


  • Item Type(s): This benchmark may be assessed using: EE item(s)

  • Assessment Limits :
    Items may include finding or describing the length of arcs when given
  • Calculator :


  • Clarification :
    Students will solve problems related to circles using the properties of
    central angles, inscribed angles, circumscribed angles, diameters,
    radii, chords, and tangents. 
  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context. 
  • Response Attributes :
    Items may require the student to use or choose the correct unit of


  • Test Item #: Sample Item 1
  • Question:

    In the diagram shown, chords AB and CD intersect at E. The measure of begin mathsize 12px style stack A C with overparenthesis on top end style is 120º, the measure of begin mathsize 12px style stack D B with overparenthesis on top end style is (2x)º, and the measure of begin mathsize 12px style angle A E C end style is (4x)º.

    What is the degree measure of begin mathsize 12px style angle A E D end style?

  • Difficulty: N/A
  • Type: EE: Equation Editor