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A square has two of its verticeson a circle and other two on a tangent to the circle. Find area of square if radius of circle is 5cm.

A square has two of its verticeson a circle and other two on a tangent to the circle. Find area of square if radius of circle is 5cm.

Grade:9

1 Answers

Ajay
209 Points
5 years ago
Let ABCD be the square with side AB on tangent .
CD will be a chord for circle.
 Let M be the mid point of CD, N be mid point of AB and O be the center of the circle, then OM will be be perpendicular to CD.
Side of the square  = radius of circle + OM = 5+OM.
SInce CD is also sdie of square M being mid point  MD = (5+OM)/2 
IN traingle OMD
OM2+MD2=OD2
OM2+ 1/4(5+OM)2 = 25
solving for OM , OM = 3.
Hence side of square = 5+3 = 8cm and area = 64cm
 
 

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