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# geometry

0
122
5

identify x

Sep 13, 2020

#1
+893
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5x = 3.5 * 13

x = 9.1        AB = 16.5          CD = 14.1

Sep 13, 2020
#3
+141
+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
#4
+2

Wrong theorem dudeguy.  The intersecting chords theorem is the one that applies.  The power point apples to a point outside the circle.

Guest Sep 14, 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.

.

Sep 13, 2020
#5
+112080
+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.