Answer:
KL = 7
Step-by-step explanation:
Given 2 secants from an external point to the circle, then
The product of the measures of one secants external part and the entire secant is equal to the product of the other secant's external part and the entire secant, that is
MN(MN + NC) = ML(ML + LK), that is
8(8 + 10x) = 9(9 + 7x) ← distribute both sides
64 + 80x = 81 + 63x ( subtract 63x from both sides )
17x + 64 = 81 ( subtract 64 from both sides )
17x = 17 ( divide both sides by 17 )
x = 1
Hence
KL = 7x = 7 × 1 = 7
The measure of the segment KL is 7 units because the sum of the external part measurements of one secant and the secant as a whole equals the sum of the external part.
It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
It is given that:
A circle with two chords shown in the picture.
As we know,
The sum of the external part measurements of one secant and the secant as a whole equals the sum of the external part measurements of the other secant and the secant as a whole.
From the figure:
MN(MN + NC) = ML(ML + LK),
8(8 + 10x) = 9(9 + 7x)
After simplifying:
64 + 80x = 81 + 63x
80x - 63x = 81 -64
17x = 17
x = 1
The measure of KL = 7x = 7(1) = 7 units
Thus, the measure of the segment KL is 7 units because the sum of the external part measurements of one secant and the secant as a whole equals the sum of the external part.
Learn more about circle here:
brainly.com/question/11833983
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