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Inscribed Angle of a Circle and its intercepted arc

Theorems and examples

    An Inscribed Angle's
  • vertex lies somewhere on the circle
  • sides are chords from the vertex to another point in the circle
  • creates an arc , called an intercepted arc
  • The measure of the inscribed angle is half of measure of the intercepted arc (This only works for the most frequently studeied case when the vetex point such as B is not within arc AC.)
    Look at the picture on the left
  • ABC is the inscribed angle
  • BC and AC are the chords
  • is the intercepted arc
  • Formula: ABC = ½  

Interactive Inscribed Angle

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Practice Identifying the Inscribed Angles and their Intercepted Arcs
Inscribed Angle Diagram
Identify the inscribed angles and their intercepted arcs
Answer

If XYZ = 40o, what is ?

Answer

Picture of inscribed angles

 

Every single inscribed angle in the picture on the left has the exact same measure, since each inscribed angle intercepts the exact same arc, which is Arc AZ?






Inscribed Angle Example

Length YZ

Length YX

Use your knowledge of the properties of inscribed angles and arcs to determine what is erronous about the picture below.
Find the error in this inscribed angle problem

 Explanation