Square ABCD is drawn with vertex C on circle A. If the radius of the circle is 8 cm, then what is the area of the square in square centimeters.
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Step-by-step explanation:
ABCD be the square inscribed by the circle.
∴OA=OB=OC=OD
ABC is a right angled triangle, as OA=8,OB=8
AB=8+8=16
According to Pythagoras theorem,
Square of hypotenuse = Sum of squares of other two sides.
AC
2
=AB
2
+BC
2
As ABCD is a square all the sides are equal, AB=BC
AC
2
=2AB
2
16
2
=2AB
2
∴AB=8
2
therefore side of the square =8
2
Area of square =(8
2
)
2
=128cm
2
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