EAch of 3 circles touch the other 2.

Circle A=radius 8cm
Circle B=radius 4cm
Circle c=radius 1cm
A triangle is formed by connecting the centers of the 3 traingles. Determine the largest angle for the traingle and which circle is the largest angle?
Also what is the area?
Please help really stumped!=[

Wouldn't the triangle have sides of 12, 9, and 5 ?

So you given 3 sides,
Use the cosine law I just showed you in your previous post.

For the area use Heron's law
A = √(s(s-a)s-b)(s-c), were a,b, c are the sides and
s = (1/2)perimeter.
s = (12+9+5)/2 = 13
s-a = 13-12 = 1
s-b = 13-8 = 5
s-c = 13-5 = 8

area = √(13x1x5x8) = √520 = appr. 22.8 cm^2

To determine the largest angle of the triangle formed by the centers of the three circles, we can use the concept of tangents and circles.

Step 1: Find the distances between the centers of the circles.
To find the distances between the centers of the circles, we need to consider the radii of the circles. Circle A has a radius of 8 cm, Circle B has a radius of 4 cm, and Circle C has a radius of 1 cm.

The distance between the centers of Circle A and Circle B is equal to the sum of their radii: 8 cm + 4 cm = 12 cm.

The distance between the centers of Circle B and Circle C is equal to the sum of their radii: 4 cm + 1 cm = 5 cm.

The distance between the centers of Circle C and Circle A is equal to the difference between their radii: 8 cm - 1 cm = 7 cm.

Step 2: Use the tangent ratio to find the angles.
Next, we can use the tangent ratio to find the angles of the triangle. The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

In our triangle, we can use the distances between the circle centers as the lengths of the sides. Let's label the vertices of the triangle as A', B', and C', corresponding to the centers of Circle A, B, and C, respectively.

The tangent of angle A' is equal to the opposite side (distance between the centers of Circle B and Circle C) divided by the adjacent side (distance between the centers of Circle C and Circle A): tan(A') = 5 cm / 7 cm ≈ 0.7143.

Similarly, the tangent of angle B' is equal to the opposite side (distance between the centers of Circle C and Circle A) divided by the adjacent side (distance between the centers of Circle A and Circle B): tan(B') = 7 cm / 12 cm ≈ 0.5833.

Finally, the tangent of angle C' is equal to the opposite side (distance between the centers of Circle B and Circle C) divided by the adjacent side (distance between the centers of Circle A and Circle B): tan(C') = 5 cm / 12 cm ≈ 0.4167.

Step 3: Determine the largest angle.
The largest angle in the triangle will have the largest tangent value. Comparing the tangent values we just calculated, we can see that the largest angle belongs to angle A' because its tangent value is the highest (0.7143).

Therefore, the largest angle in the triangle is angle A', which corresponds to the center of Circle A.

Step 4: Calculate the area of the triangle.
To calculate the area of the triangle, we can use Heron's formula, which states that the area of a triangle with sides a, b, and c is given by:

Area = √(s * (s - a) * (s - b) * (s - c))

Where s is the semi-perimeter of the triangle, given by:

s = (a + b + c)/2

In our case, the sides of the triangle are the distances between the centers of the circles:

a = 7 cm
b = 5 cm
c = 12 cm

Using the formula, we can calculate the semi-perimeter:

s = (7 cm + 5 cm + 12 cm)/2 = 24 cm/2 = 12 cm

And then, we can calculate the area:

Area = √(12 cm * (12 cm - 7 cm) * (12 cm - 5 cm) * (12 cm - 12 cm)) = √(12 cm * 5 cm * 7 cm * 0) = 0 cm²

Therefore, the area of the triangle formed by the centers of the three circles is 0 cm².