MathDB

5

Part of 2020 South Africa National Olympiad

Problems(1)

SAMO Problem 5: Cyclic quadrilateral through points of two isosceles triangles

Source: South African Mathematics Olympiad 2020, Problem 5

1/17/2021
Let ABCABC be a triangle, and let TT be a point on the extension of ABAB beyond BB, and UU a point on the extension of ACAC beyond CC, such that BT=CUBT = CU. Moreover, let RR and SS be points on the extensions of ABAB and ACAC beyond AA such that AS=ATAS = AT and AR=AUAR = AU. Prove that RR, SS, TT, UU lie on a circle whose centre lies on the circumcircle of ABCABC.
geometrycyclic quadrilateralcircumcircle