#1

#3**+2 **

The theorem used is called the power of a point theorem. More about that here: https://en.wikipedia.org/wiki/Power_of_a_point

thedudemanguyperson
Sep 13, 2020

#2**+2 **

*Identify the value of x and the length of each chord.*

The "Intersecting Chords Theorem" states

The intersecting chords theorem or just the chord theorem is a statement in elementary geometry

that describes a relation of the four line segments created by two intersecting chords within a circle.

It states that the products of the lengths of the line segments on each chord are equal.

I hadn't known this before. A tip of the hat to jugoslav.

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Guest Sep 13, 2020

#5**+2 **

Thanks guest, I did not remember that one either.

It is actually very easy to prove,

You do have to start with the knowledge that 2 angles within a circle, both with their apex on the circumference, will be equal if they stand on the same arc.

And here is a you tube clip explaining it.

Melody Sep 15, 2020