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## Geometry (Eureka Math/EngageNY)

### Unit 5: Lesson 1

Topic A: Central and inscribed angles- Inscribed angles
- Inscribed angles
- Challenge problems: Inscribed angles
- Inscribed angle theorem proof
- Inscribed angle theorem proof
- Proof: Right triangles inscribed in circles
- Inscribed shapes: find diameter
- Inscribed shapes: angle subtended by diameter
- Inscribed shapes: find inscribed angle
- Inscribed shapes
- Challenge problems: Inscribed shapes
- Inscribed quadrilaterals proof
- Solving inscribed quadrilaterals
- Inscribed quadrilaterals
- Geometric constructions: circle-inscribed square
- Geometric constructions: circle-inscribed equilateral triangle
- Geometric constructions: circle-inscribed regular hexagon
- Proof: radius is perpendicular to a chord it bisects
- Proof: perpendicular radius bisects chord

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# Inscribed angles

CCSS.Math:

Sal finds a missing inscribed angle using the inscribed angle theorem.

## Video 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.