2024 · Q49
In a quarter circle of radius R, a circle of radius r is inscribed. What is the ratio of R to r ?
Elementary MathematicsCircles
- A(2 + 1) : 1
- B(3 + 1) : 1
- C3 : 2
- D5 : 4
Explanation
Let the small circle touch both straight radii and the arc of the quarter circle. Then R = r + r√2, i.e. R : r = (√2 + 1) : 1. This is option (a) as printed.