MathDB
2024 Geo Problem 3

Source:

April 15, 2024
geometry

Problem Statement

Circles C1C_1, C2C_2, and C3C_3 are inside a rectangle WXYZWXYZ such that C1C_1 is tangent to WX\overline{WX}, ZW\overline{ZW}, and YZ\overline{YZ}; C2C_2 is tangent to WX\overline{WX} and XY\overline{XY}; and C3C_3 is tangent to YZ\overline{YZ}, C1C_1, and C2C_2. If the radii of C1C_1, C2C_2, and C3C_3 are 11, 12\tfrac 12, and 23\tfrac 23 respectively, compute the area of the triangle formed by the centers of C1C_1, C2C_2, and C3C_3.
Proposed by Connor Gordon