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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.
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 OMDOM2+MD2=OD2OM2+ 1/4(5+OM)2 = 25solving for OM , OM = 3.Hence side of square = 5+3 = 8cm and area = 64cm
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