Inscribed Angle of a Circle and its intercepted arc

Theorems and examples

If XYZ = 40^o, what is ?

Measure of inscribed angle = ½ measure of the intercepted arc
Therefore, = 2 × 40^o = 80^o

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 ?

Length YZ

YZ²=5²+12²

YZ = 13

Length YX

Use your knowledge of the properties of inscribed angles and arcs to determine what is erronous about the picture below.


 Explanation  

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°.