Question

A Square ABCD inscribed in a circle of radius 4cm. What is the minor segment cut off by the chord AB

Answers

Reiny
When you ask, "What is the minor segment cut off by the chord AB", I will assume
you meant its area.
sketch the square in the circle.
draw its two diagonals
area of the sector with arc AB = (1/4)π(4^2) = 4π square units
area of the right-angled triangle with AB as its hypotenuse
= (1/2)(4)(4) = 8 square units

So area of segment formed = 4π - 8 square units= appr .....

or , even easier way:
Area of circle = 16π
area of square: let each side of the square be x
x^2 + x^2 = 8^2
x^2 = 32
area = 32
area of one of the 4 segments = (1/4)(16π-32) = 4π - 8
Jocabed
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Efrata
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