In this unit, you studied a handful of circle theorems. However, there are other circle theorems not covered in this unit or course. Do some research online or in textbooks to uncover a circle theorem (or more than one) that wasn’t presented in this unit. Describe it in detail. Then write either a two-column proof or a paragraph proof for the theorem.

Does the theorem that you proved relate to theorems that you previously studied? If so, how? Were you able to apply some theorems that you proved earlier to your newfound theorem? Explain. How might your theorem be used in a real-world application?

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In this unit, you studied a handful of circle theorems. However, there are other circle theorems not covered in this unit or course. Do some research online or in textbooks to uncover a circle theorem (or more than one) that wasn’t presented in this unit. Describe it in detail. Then write either a two-column proof or a paragraph proof for the theorem.

Does the theorem that you proved relate to theorems that you previously studied? If so, how? Were you able to apply some theorems that you proved earlier to your newfound theorem? Explain. How might your theorem be used in a real-world application?

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Topeadeniran2go Topeadeniran2go · Answer 1

Topeadeniran2go Topeadeniran2go

It should be noted that the angle at the center of the circle is twice the angle at the circumference.

Circle Theorem

It should also be noted that the angle in a semicircle is a right angle. Angles that are in the same segment are equal.

Furthermore, the opposite angle that is in a cyclic quadrilateral sum is 180°. The angle between the chord and the tangent is also equal to the angle in the alternate segment.

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