Question

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

• A. Area of SPQT = Area of RUVZ = Area of PXWR
• B. Area of SPQT = Area of PXWR − Area of RUVZ
• C. Area of PXWR = Area of SPQT − Area of RUVZ
• D. Area of PXWR = Area of RUVZ − Area of SPQT

Hint:

In problems involving areas of squares inscribed within a circle, the relationships between the areas are often governed by the tangents and the distances between the center and the points of tangency.

Answer 1

The Correct Option is B

In the given diagram, we are working with areas of squares inscribed in a circle. The points and lines are defined such that:
- The area of the square \( PXWR \) is the area enclosed by the tangent line \( PX \) and the radial line from the center \( R \).
- Similarly, the areas of the other squares \( RUVZ \) and \( SPQT \) are determined by the distances defined by the lines and the tangents.
By analyzing the geometric relationships and using the fact that the squares are inscribed, the correct relation between the areas of these squares is: \[ \text{Area of SPQT} = \text{Area of PXWR} - \text{Area of RUVZ}. \] This is derived from the fact that the areas of the squares depend on the lengths of the sides, and the side lengths are related in such a way that this equation holds. Therefore, the correct answer is (B).