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
Practice Identifying the Inscribed Angles and their Intercepted Arcs
Identify the inscribed angles and their intercepted arcs
If XYZ = 40o, what is ?
Measure of inscribed angle = ½ measure of the intercepted arc
Therefore, = 2 × 40o = 80o
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 ?
Use your knowledge of the properties of inscribed angles and arcs to determine what is erronous about the picture below.
The error is that 992 +1322 ≠ 1642. Since the pythagoren theorem does not hold, the X is not a right angle and the measure of arc ≠ 180°.