A chord AB divides a circle of radius 4 cm into two segments. If AB subtends a central angle of 60°, find the area of the minor segment.

Step-by-step explanation:

The diagram of the circle is shown in the attached photo.

Looking at triangle AOB, 2 sides are equal. It means that A= B.

Therefore, A = B = (180 - 60)/2 = 60

Therefore, triangle AOB is an equilateral triangle. AB = AO = BO = 4 cm

We would find the area of triangle AOB by applying heron's formula

Area = √s(s - a)(s - b)(s - c)

s = (a + b + c)/2 = (4 + 4 + 4)/2 = 6

Area = √6(6 - 4)(6 - 4)(6 - 4)

Area = √48 = 6.93cm²

Area of sector formed by the minor segment = area of triangle + area of minor segment

Area of sector = 60/360 × 3.14 × 4² = 8.37 cm²

Area of minor segment = 8.37 - 6.93 = 1.44 cm²

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