Question

Find the area of the square that can be inscribed in a circle of radius 8 cm.

Answer 1

Step-by-step explanation:

Let 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

Answered By

Answer 2

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Let 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 ^22

 

16^2 =2AB^2

 

∴AB=8^2

​  

 

Therefore side of the square =8^2 .

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