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GATE 2022 BT – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

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

source diagram and its labels are reproduced in the attached image.
  1. Area of SPQT = Area of RUVZ = Area of PXWR
  2. Area of SPQT = Area of PXWR − Area of RUVZ
  3. Area of PXWR = Area of SPQT − Area of RUVZ
  4. Area of PXWR = Area of RUVZ − Area of SPQT

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Show answer and explanation

Correct answer: (B) Area of SPQT = Area of PXWR − Area of RUVZ

Explanation

The radius to tangency is perpendicular to the tangent, so $PQ^2=PR^2-RQ^2$. The squares on these sides give SPQT=PXWR−RUVZ.