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identify x

 

 Sep 13, 2020
 #1
avatar+240 
+2

5x = 3.5 * 13

 

x = 9.1        AB = 16.5          CD = 14.1

 Sep 13, 2020
 #3
avatar+132 
+1

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
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+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
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+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
avatar+111127 
+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.

 

https://www.youtube.com/watch?v=CxvOx71nne4

 Sep 15, 2020

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