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.

Question

Ajay · Answer

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 OM 2 +MD 2 =OD 2 OM 2 + 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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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.

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