+600 The theorem used is called the power of a point theorem. More about that here: https://en.wikipedia.org/wiki/Power_of_a_point
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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+118609 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.
