Question

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

Answer 1

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.

`(OK)/(NL)=(KM)/(LM)`

`(12)/(8)=(x+20)/(x)`

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

12x = 8x + 160

12x - 8x = 160

4x = 160

x = 40