In the following diagram, the point B is the center of the circle. The lines PQ and VW are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ, and SFQT is A. Area of SFQT = Area of PXWR - Area of RUVZ B. Area of SFQT + Area of RUVZ = Area of PXWR C. Area of SFQT = Area of RUVZ D. None of the above

GATE 2022 · General Aptitude · Squares · medium

Answer: Area of SFQT + Area of RUVZ = Area of PXWR (option B).

1. Assign variables to half-sides of each square: Let half-side of PXWR = a (area = 4a^2), of RUVZ = r (area = 4r^2), of SFQT = b (area = 4b^2). The circle has radius r.
2. Apply Pythagorean theorem at center B: The right triangle at B has legs b (from center to side of SFQT = half-side of SFQT) and r (radius to tangent point on PQ/VW), with hypotenuse a (from center to corner of PXWR). So a^2 = b^2 + r^2.
3. Convert to area relation: Multiply through by 4: Area(PXWR) = Area(SFQT) + Area(RUVZ).