MathDB
Circle inscribed

Source: UMD 2023 I #11

October 24, 2023
UMDgeometry

Problem Statement

Let S1S_1 be a square with side ss and C1C_1 be the circle inscribed in it. Let C2C_2 be a circle with radius rr and S2S_2 be a square inscribed in it. We are told that the area of S1C1S_1 - C_1 is the same as the area of C2S2.C_2 - S_2. Which of the following numbers is closest to s/r?s/r? a. 1b. 2c. 3d. 4e. 5 \mathrm a. ~ 1\qquad \mathrm b.~2\qquad \mathrm c. ~3 \qquad \mathrm d. ~4 \qquad \mathrm e. ~5