About this video
A circle is centered at B with central angle ABC measuring 132 degrees. The video shows that inscribed angle ADC intercepts the same arc AC, so by the inscribed angle theorem it measures half of 132, which is 66 degrees.
You'll be able to
- tell a central angle from an inscribed angle.
- identify when two angles intercept the same arc.
- use the inscribed angle theorem to find an inscribed angle from a central angle.
Key words
- central angle
- An angle whose vertex is at the center of the circle.
- inscribed angle
- An angle whose vertex sits on the circle and whose sides are chords.
- intercepted arc
- The arc that lies between the two sides of an angle.
- inscribed angle theorem
- An inscribed angle measures half of the central angle that intercepts the same arc.
Transcript
- [Voiceover] A circle is centered on point B. We see that right over there. That's the center of this big, blue circle. Points A, C, and D lie on its circumference. We see that. Points A, C, and D lie on the circumference. If angle ABC... So ABC; So that's this central angle right over here; measures 132 degrees.
Alright, so this is 132 degrees. What does angle ADC measure? A, D, C. So let's think about how these are related. ABC is a central angle. ADC is an inscribed angle. And they intercept the same arc. The arc AC. They both intercept this arc right over here. And we know from the inscribed angle theorem that an inscribed angle that intercepts the same arc as a central angle is going to have half the angle measure.
And it even looks that way right over here. So if ABC- if the central angle is 132 degrees, then the inscribed angle that intercepts the same arc is going to be half of that. So half of 132 degrees is what? It is 66 degrees. We can check our answer, and we got it right.
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