MathDB

G4

Part of 2013 Balkan MO Shortlist

Problems(1)

concurrency wanted, 2 circles and tangents related

Source: Balkan MO Shortlist 2013 G4 BMO

3/3/2020
Let c(O,R)c(O, R) be a circle, ABAB a diameter and CC an arbitrary point on the circle different than AA and BB such that ∠AOC>90o\angle AOC > 90^o. On the radius OCOC we consider point KK and the circle c1(K,KC)c_1(K, KC). The extension of the segment KBKB meets the circle (c)(c) at point EE. From EE we consider the tangents ESES and ETET to the circle (c1)(c_1). Prove that the lines BE,STBE, ST and ACAC are concurrent.
geometrycirclesconcurrencyconcurrent