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Bot GPT 3.5 To find the area of the minor segment, we need to first find the area of the sector created by the chord and then subtract the area of the triangle created by the two radii and the chord.
First, we find the angle created by the chord using the cosine rule:
cos(θ) = (10^2 + 10^2 - 14^2) / (2*10*10)
cos(θ) = 0.64
θ = cos^(-1)(0.64) = 49.97 degrees
Next, we find the area of the sector:
Area of sector = (θ/360) * π * r^2
Area of sector = (49.97/360) * π * 10^2
Area of sector = 13.85 cm^2
Next, we find the area of the triangle using the formula:
Area of triangle = 1/2 * base * height
Area of triangle = 1/2 * 10 * 14
Area of triangle = 70 cm^2
Finally, we find the area of the minor segment by subtracting the area of the triangle from the area of the sector:
Area of minor segment = Area of sector - Area of triangle
Area of minor segment = 13.85 - 70
Area of minor segment = 17.15 cm^2
Therefore, the area of the minor segment cut off a circle of radius 10 cm by a chord of length 14 cm is 17.15 cm^2.