# Find the length of XC

Anonymous
account_balance_wallet \$5

### Question Description

psumanrec
School: UCLA

It can be solved using the following theorem which is secant theorem

"If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the product of the length of the other secant segment and its external part."

Here the same point is G.

Using the above theorem

GH*DG=FG*EG

We have DG=x+3+5=x+8

GH=5

FG=6

GE=x+6

Thus

(x+8)5 =6(x+6)

Solve for x

5x+40=6x+36

x=4

If you are satisfied then rate my answer so that I can help you in the future more.Thanks :)

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Anonymous
Excellent job

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