A Unit circle has center at (5,0) and second circle with a radius 2 units has its center at (17,0). A common tangent to both circles intersects x-axis at Q(a,0) what is value of a
+128475 We can use similar triangles here
Let A be the center of the smaller circle and B the center of the larger circle
Let BC = radius of the larger circle AD = radius of smaller cirlce
And triangles BCQ and ADQ are similar
Let AB be the distance between the circles' centers = 12
And let x + 1 the distance betwen A and Q
We have this
BQ / BC = AQ / AD
(12 + 1 + x) / 2 = (1 + x) / 1 simplify
13 + x = 2 (1 + x)
13 + x = 2 + 2x
13 - 2 = x
11 = x
Q = (a , 0) = ( 5 - (1 + x) , 0) = ( 5 - (12) , 0) = (-7, 0)
