10-11.5

Part of 2021 Sharygin Geometry Olympiad

Problems(1)

4 intersection points lie on a circle coaxial with two given circles

Source: 2021 Sharygin Geometry Olympiad Finals grades X-XI p5

A secant meets one circle at points

A_1

B_1

։, this secant meets a second circle at points

A_2

B_2

. Another secant meets the first circle at points

C_1

D_1

and meets the second circle at points

C_2

D_2

. Prove that point

A_1C_1 \cap B_2D_2

A_1C_1 \cap A_2C_2

A_2C_2 \cap B_1D_1

B_2D_2 \cap B_1D_1

lie on a circle coaxial with two given circles.

Concycliccoaxial circlesgeometry