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Take it just as asking, "Which of the following are

#40 is a fairly direct application of some circle theorems. Focus on x first. Label the diagram with the given arc measures, ignoring the tangent at C. What theorem applies?

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In addition to Prof Peterson's comments, see here for properties of the isosceles trapezoid. It seems the question is going for the diagonals have equal lengths. However, depending upon the sizes of \(\displaystyle a,~\&~b\) the formulae are ambiguous.Hi everyone I am studying for a Geometry test out and i was doing the problems on the online practice quizzes and i had 2 that i got stuck on

Can someone explain them that would be super helpful

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For the other, let \(\displaystyle D\) be the point of intersection of \(\displaystyle \overrightarrow {AC} \) with the circle.

Then \(\displaystyle y\) is one-half the measure of \(\displaystyle arc{CD}\).

And \(\displaystyle m(\angle A)=\frac{m(arc{BC})-x}{2}\)

thanks for the explanations they were very helpful

i have a different problem which i think is right but it says my answer is wrong

i'm pretty sure there is a theorem that says that two inscribed angles that intercept the same arc are congruent

here angle BAC and BOC are the inscribed angles and they both share arc BC but why are they not congruent angles?

maybe i'm being stupid

i have a different problem which i think is right but it says my answer is wrong

i'm pretty sure there is a theorem that says that two inscribed angles that intercept the same arc are congruent

here angle BAC and BOC are the inscribed angles and they both share arc BC but why are they not congruent angles?

maybe i'm being stupid

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Do these angles LOOK congruent to you?

A theorem says that an

[There is another theorem that an