Question

What is the minor segment out of the circle of radius 10 cm by the chord of length 14 cm?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The minor segment can be calculated by subtracting the area of the triangle formed by the chord and the two radii from the sector of the circle.

The area of the sector is given by:
Sector Area = (θ/360) * πr^2
where θ is the central angle in degrees (in this case, the central angle would be 360 - 2*arcsin(7/10)*180/π), r is the radius of the circle.

Next, we need to calculate the area of the triangle formed by the chord and the two radii.
Since the chord divides the circle into two equal parts, the triangle can be divided into two right triangles.
Using the Pythagorean theorem, the height of the triangle can be calculated as:
h = sqrt(r^2 - (7)^2)

The area of the triangle is:
Triangle Area = 1/2 * base * height = 1/2 * 14 * sqrt(10^2 - 7^2)

Finally, by subtracting the area of the triangle from the sector, we can find the area of the minor segment.