Two equal corcles intercept each other. Find the area of the overlapping region, if the radii of the circles are 10 cm each and the distance beten centers also equals 10 cm.
How do i solve this? Thank u in advance.
To find the area of the overlapping region of two equal circles, you can follow these steps:
1. Draw a diagram: Start by drawing two circles with the given radii (10 cm each) and draw a line connecting their centers.
2. Identify the distance between the centers: In this case, the distance between the centers is given as 10 cm.
3. Determine the intersection points: Since the distance between the centers is equal to the sum of the radii (10 cm each), the circles will just touch each other. Hence, they will have two intersection points.
4. Find the angle between the radii at each intersection point: To do this, calculate the central angle at the center of each circle that intercepts one of the intersection points. The central angle can be found using the formula θ = 2 * arccos(d/2r), where θ is the central angle, d is the distance between the centers, and r is the radius of the circles.
5. Find the area of each sector: The area of a sector can be calculated using the formula A = (θ/360) * π * r^2, where A is the area of the sector, θ is the central angle in degrees, π is a constant approximately equal to 3.14159, and r is the radius of the circle.
6. Calculate the area of the overlapping region: Subtract the areas of the two sectors from the sum of their areas to find the area of the overlapping region.
In this particular case, the circles only touch each other, so the angle between the radii is 0 degrees at both intersection points. Hence, the overlapping region is just the two areas of the circles combined.
To calculate the area of the overlapping region, you can use the formula A = π * r^2, where A is the area and r is the radius of each circle. In this case, A = π * (10 cm)^2 = 100π cm^2.