Question

Step 3: Let LM = x. We know the lengths of the radii of each circle, so KL = 12 +

Answer 1

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.

$\frac{OK}{NL}=\frac{KM}{LM}$

$\frac{12}{8}=\frac{x+20}{x}$

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

12x = 8x + 160

12x - 8x = 160

4x = 160

x = 40