MathDB

G1

Part of 2016 Romanian Master of Mathematics Shortlist

Problems(1)

length of segment is equal to diameter , starting wiith intersecting circles

Source: RMM Shortlist 2016 G1

7/4/2019
Two circles, ω1\omega_1 and ω2\omega_2, centred at O1O_1 and O2O_2, respectively, meet at points AA and BB. A line through BB meets ω1\omega_1 again at CC, and ω2\omega_2 again at DD. The tangents to ω1\omega_1 and ω2\omega_2 at CC and DD, respectively, meet at EE, and the line AEAE meets the circle ω\omega through A,O1,O2A, O_1, O_2 again at FF. Prove that the length of the segment EFEF is equal to the diameter of ω\omega.
geometrycirclesTangentsdiameter