2023 · Q95
Consider the following for the next three (03) items that follow: A circle of radius 10 cm is inscribed in a square PQRS. A rectangle measuring 4 cm × 2 cm is drawn at the corner P, and a smaller square is drawn at the corner R. What is the area of the smaller square?
Elementary MathematicsCircles
- A50(3 - √2) square cm
- B25(3 - 2√2) square cm
- C25(3 + 2√2) square cm
- D50(3 - 2√2) square cm
Explanation
The square PQRS has side 20 cm; the corner R is 10√2 from the centre O. The smaller square's far vertex touches the circle along the diagonal, so s√2 = 10√2 − 10, giving s = 10 − 5√2. Its area is s² = 150 − 100√2 = 50(3 − 2√2) square cm (D).