Answer:
a = 1.5
VW = 9 ft
Step-by-step explanation:
Since the tangent lines connect both circles, we know that the line VU and VX are congruent (equal). Thus, we can set them equal to each other and solve for a:
a + 4 = a² + 0.25 Set equal
a² - a = 3.75 Isolate a values
a² - a + 0.25 = 3.75 + 0.25 Complete the square
(a + 0.5)² = 4 Factor
a + 0.5 = 2 Simplify
a = 1.5
Now we need to calculate VW, but thats easy because its equal to TV, and since we know a, we can just plug it in:
((1.5) + 7.5) ft
9 ft
