In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

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Area of PXWR = Area of RUVZ – Area of SPQT

Area of PXWR = Area of SPQT – Area of RUVZ

Area of SPQT = Area of PXWR – Area of RUVZ

Area of SPQT = Area of RUVZ = Area of PXWR

Answer (Detailed Solution Below)

Option Area of SPQT = Area of PXWR – Area of RUVZ is correct

Detailed Explanation

From \triangledown \; PQR by Pythagoras theorem,

\Rightarrow {PR}^2 = {PQ}^2 + {QR}^2

Also, QR = RZ ,

\Rightarrow {PR}^2 = {PQ}^2 + {RZ}^2

\Rightarrow \text {Area \, of \,} PXWR = \text {Area \,of \,} SPQT +\text{ Area \,of \,} RUVZ

\Rightarrow \text {Area \, of \,} SPQT = \text {Area \, of \, } PXWR \,- \,\text {Area\, of\,} RUVZ

Correct option is : Area of SPQT = Area of PXWR – Area of RUVZ

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