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### Course: Class 10 > Unit 8

Lesson 5: Angle subtended by a chord/arc of a circle# Inscribed angles

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

## Want to join the conversation?

- At0:46, Sal says that "we know from the inscribed angle theorem ...."

What exactly is the inscribed angle theorem? Is there another video somewhere that I missed, because I am doing this mission from the beginning? If not, is there a link somewhere that explains this concept?(41 votes)- The inscribed angle theorem states that the inscribed angle has one half the degree of the central angle that shares the same arc with the inscribed angle. The theorem is explained later in the video.(13 votes)

- Can someone please explain? I think I need some help on this.(5 votes)
- Hey man this theorem is also called the double angle theorem. It states that 'the angle subtended by an arc at the center is double of the angle subtended by it at the center'. To put is simply the angle ADC(from the video) is half(1/2) of angle ABC. Hope it make your doubt clear!(5 votes)

- im confused is there a different way(4 votes)
- If you are trying to find the blue angle, double the orange angle. If you are trying to find the orange angle, halve the blue angle.

Hope that helps!(9 votes)

- i dont understand any of this circle geometry stuff?(4 votes)
- hey!!

go back and start from the first video and search on the net for more videos

if u practice more then you will be able to master it(4 votes)

- Don't we actually calculate the angle using Θ=arc length/radius? As the radius(distance) is doubled (=diameter in that case), initial Θ is multiplied by 1/2.(3 votes)
- Hi lived4adream, the answer is no, we don't. The ratio you are talking about is the radian measurement(arc length/radius). Radians are not used for inscribed angles; their purpose is to resemble and serve as a unit of measurement for the central angle derived from the ratio of the arc
**length**of a central angle and the**radius**of the circle. Besides, in this case, AD and CD are not diameters of circle B. The basis of the inscribed angle theorem is a bit more complicated and different from what you are thinking of.

Overall, great question!

Hope you found this helpful and feel free to ask if you have any more questions!

~Hannah(4 votes)

- What is the definition of
*inscribed angle*?(3 votes)- An inscribed angle is the angle formed in the interior of a circle when two chords intersect the same arc.(1 vote)

- when he says <ABC he takes it the way show in the video. my question is, why should we not take the other angle i.e., the greater angles more than 180 one?(2 votes)
- If you refer to0:15; you could understand by other way that it is the angle of intersection between the line AB and line BC at the vertex B.

and by common thinking and stated in this course before we measure the less angle (angle is corner in latin) unless the problem define the opposite

please refer to https://www.khanacademy.org/math/basic-geo/basic-geo-angle/modal/v/angle-basics(3 votes)

- How would you know If it's an inscribed Angles in the first place?(2 votes)
- An inscribed angle is anywhere on the circle where 2 secant segments intersect(2 votes)

- ADC is half of ABC, it's a formula? Do u have anyway to prove it? Thank you(1 vote)
- this has nothing to do with the questions in the exercise?(2 votes)

## 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.