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GATE 2022 PH – 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

Circle with tangents and squares on the sides of a right triangle.
  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 tangent is perpendicular to the radius, so PR squared equals PQ squared plus RQ squared. Rearrangement gives the area of SPQT as PXWR minus RUVZ.