Have lots of fun with this cool idea!

Okay, but that was just a proof for the case when an angle contains a diameter. What about for any old angle? Does it all break down?!?!

Luckily, the Inscribed Angle Theorem is true for any angle. Take a look at the proof below.

There's even another case that we haven't covered yet. When the angle has one side that is a tangent to the circle and one side going through the circle (called a *secant* line), with its vertex still on the circle, its measure is still half of the measure of its inscribed arc.

I really do think we've covered all the cases now! Now, you're all ready to do some geometry problems involving inscribed arcs and angles!

Some more visual examples of different inscribed angles: secant-secant inscribed angles, secant-tangent inscribed angles, and tangent-tangent inscribed angles.

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