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Work Shown:
There are two chords here and they are AB and CD. They intersect at point P.
By the intersecting chords theorem, we can say the following
AP*PB = CP*PD
which is basically saying "the product of the pieces of each chord is the same for both chords"
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So,
AP*PB = CP*PD
10*x = 8*(3+x)
10x = 24+8x
10x-8x = 24
2x = 24
x = 24/2
x = 12
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We can see that
AP*PB = 10*x = 10*12 = 120
and also
CP*PD = 8(3+x) = 8(3+12) = 8*15 = 120
So both products are 120 showing that AP*PB = CP*PD is a true equation when x = 12. We have confirmed the answer.
