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SE=SF wanted , 3 circles ext. tangent

Source: Polish MO Recond Round 1992 p4

September 9, 2024
geometrycirclesequal segments

Problem Statement

The circles k1k_1, k2k_2, k3k_3 are externally tangent: k1k_1 to k2k_2 at point AA, k2k_2 to k3k_3 at point BB, k3k_3 to k4k_4 at point CC, k4k_4 to k1k_1 at point DD. The lines ABAB and CDCD intersect at the point SS. A line p p is drawn through point S S , tangent to k4 k_4 at point F F . Prove that ∣SE∣=∣SF∣ |SE|=|SF| .
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