Two triangles can be formed with the given information. Use the Law of Sines to solve the trianglesusing the law of sines.C=7 A37degrees B71degrees
+128475 See the following image :
We can use similar triangles to solve this
Let X be the number of units on the x axis that is to the left of the point (-3,0)
Let A = (0,0) Let B = (7,0)
The radius of the smaller circle = 3 = AC the radius of the large circle = 4 = BD
BX = 10 + X
AX = 3 + X
We have that
BX / BD = AX / AC
(10+ X) / 4 = ( 3 + X) / 3 cross-multiply
3 (10 + X) = 4(3 + X)
30 + 3X = 12 + 4X
30 - 12 = 4X - 3X
18 = X
The the coordinates of X are ( -3 - 18, 0) = ( -21, 0 )
We can find XC as sqrt ( 21^2 - 3^2) = 12sqrt (3)
The tangent of angle XAC = -3 / ( 12 sqrt 3) = -1 ( 4sqrt (3)) = -sqrt (3) / 12
The equation of one of the tangent lines is
y = (-sqrt (3) / 12) ( x + 21)
And the equation of the other is just y= (sqrt (3) / 12) (x + 21)
