Area of a circle with a line running through it

Question

I really just need the answer for construction project.have a circle with a diameter of 23. and a straight line running through the circle 4 from the edge. need the area of each portion on either side of the circle

Answer 1

The area of circle = (pi) r² where "r" is the length of the radius. A straight line segment that goes through the center of a circle and hits the circumference of the circle twice is known as the diameter of a circle. The diameter is called "d" and

d= 2r so the length of the diameter is twice the length of the radius.

Is this other segment in the circle a ray? I would like for you to restate the question because some details of the image are not clear. Or possibly included a visual. Does the ray intersect the diameter ?

Answer 2

It's really hard to determine what you mean. If you are talking about something like this:

To calculate the area of the sector formed where the circle intersects the red line, you could create a triangle and then use trig to find the central angle. You would get cos^-1(7.7/11.5) = 49.294° then double it to get the full angle meaning the central angle of the sector would be 98.588°. Then to calculate the area of the sector you would use (98.588/360)π•r² and with r = 11.5 the area of the sector is 113.781. You could then calculate the area of the triangle you used earlier with A = 1/2•b•h. You could use the Pythagorean Theorem to find the base b/2 = √(11.5² - 7.5²) = 8.7178 so the base is 2•8.7178 = 17.4356 and the area of the triangle would be 1/2(17.4356)(7.5) = 65.3835. The area under the line is then 113.781 - 65.3835 = 48.3975.

The area of the whole circle is π•r² = π•(11.5)² = 415.4756 so the area above the line is 415.4756 - 48.3975 = 367.078

But I don't even know if this is the right sketch for the problem.