a circle of diameter 80mm and a line BC. The ratio of the circle to the line BC is 7:5. what is the true length of the line from the center of the circle.2. what is the actual diamter of the cirlce.

thanks

To find the true length of the line from the center of the circle, we can use the concept of similar triangles.

1. Let's denote the length of the line BC as x. According to the given ratio, the circle to line BC ratio is 7:5. This means that the radius of the circle to line BC ratio is also 7:5. Since the diameter of the circle is given as 80mm, the radius will be half of that, which is 40mm (diameter / 2).

2. To find the true length of the line from the center of the circle, we can set up a proportion using the similar triangles formed by the radius of the circle, the true length of the line, and the given line BC. The proportion will be:

(radius of the circle) / (true length) = (line BC) / (x)

Substituting in the given values, we have:

40mm / (true length) = x / 80mm

To solve for the true length, we can cross-multiply and then divide:

40mm * 80mm = (true length) * x

3200 = (true length) * x

Dividing both sides by x:

(true length) = 3200 / x

Therefore, the true length of the line from the center of the circle is 3200 / x.

3. To find the actual diameter of the circle, we can simply double the given value of the radius. Since the radius is 40mm, the actual diameter will be 2 * 40mm = 80mm.

So, the true length of the line from the center of the circle is 3200 / x, and the actual diameter of the circle is 80mm.