9514 1404 393
Answer:
5) x = 15
6) NL = 40
Explanation:
The product of the length of the external segment and the whole segment is the same for each secant.
5) 8(8+19) = 9(9 +x)
24 = 9+x . . . . . . . . . divide by 9
x = 15
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6) 10(10+42) = 13(NL)
10(52)/13 = NL = 40 . . . . . divide by 13
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Additional comment
I like to remember as few rules as possible. If you look at the rule used in problems 3 and 4, you see that the constant for each chord is the product of lengths from the point of intersection to the two points of intersection with the circle.
If you look at the rule used in problems 5 and 6, you see that it can be expressed the same way: the constant for each secant is the product of lengths from the point of intersection of the secants (now external to the circle) to the two points of intersection with the circle.
The one additional rule that applies to this sort of geometry is the rule that is used when one of the "secants" is a tangent. In that case, you can consider the two points of intersection with the circle to be the same point, so the product of the lengths is the square of the length of the tangent.
Now, you have one rule that you can use for all three cases. I find it easier to remember that way.