MathDB

5

Part of 1989 Mexico National Olympiad

Problems(1)

centers of 4 circles are vertices of a rectangle

Source: Mexican Mathematical Olympiad 1989 OMM P5

7/27/2018
Let C1C_1 and C2C_2 be two tangent unit circles inside a circle CC of radius 22. Circle C3C_3 inside CC is tangent to the circles C,C1,C2C,C_1,C_2, and circle C4C_4 inside CC is tangent to C,C1,C3C,C_1,C_3. Prove that the centers of C,C1,C3C,C_1,C_3 and C4C_4 are vertices of a rectangle.
geometryrectangletangent circles