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Step 3: Let LM = x. We know the lengths of the radii of each circle, so KL = 12 +
8 = 20. Add the length of KL to the diagram.
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12 K
20
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12
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8
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Step 3 Let LM x We know the lengths of the radii of each circle so KL 12 8 20 Add the length of KL to the diagram J 12 K 20 L X M 12 00 8 N class=

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Answer:

Step-by-step explanation:

Step 3:

Let LM = x

OK = KP = 12 units [Radii of circle K]

LN = LP = 8 units [Radii of circle L]

Therefore, KL = KP + PL

KL = 12 + 8

     = 20 units

Step 4:

Since, ΔKOM and ΔLNM are the similar triangles,

By the property of two similar triangles, corresponding sides of these similar triangles will be proportional.

[tex]\frac{OK}{NL}=\frac{KM}{LM}[/tex]

[tex]\frac{12}{8}=\frac{x+20}{x}[/tex]

12x = 8(x + 20) [By cross multiplication]

12x = 8x + 160

12x - 8x = 160

4x = 160

x = 40

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