Question

Two circles, C and Cr intersect each other. C's radius is 1, while Cr's radius is r. Their tangent lines form an internal angle of 120° at each intersection point. 1) Calculate the distance d in terms of r. 2) Find where d has a maximum or a minimum. 3) Find the area of the intersection in terms of π

Answer 1

Here's what I have done to find d in terms of r... by using the law of cosines,I have that d² = 1² + r² -2rcos(120). Is this right?

Answer 2

Using implicit differetiation.\[2dd^{\prime} = 2r + 2 \rightarrow d^{\prime}=\frac{2r+2}{\sqrt{r²+2r+1}}\] but 2r+2 =0 gives a negative number! What have I done wrong?

Answer 3

can you label it?

Answer 4

shouldn't make their radius look like equal, draw on my pic, please

Answer 5

middle is d, one sec, switching pcs

Answer 6

and label the angle, too