MathDB

2020.11.2

Part of Kyiv City MO Seniors Round2 2010+ geometry

Problems(1)

<TSC=<BAC wanted, parallelogram, circumcircle (2020 Kyiv City MO Round2 11.2)

Source:

9/21/2020
A point PP was chosen on the smaller arc BCBC of the circumcircle of the acute-angled triangle ABCABC. Points RR and SS on the sidesAB AB and ACAC are respectively selected so that CPRSCPRS is a parallelogram. Point TT on the arc ACAC of the circumscribed circle of △ABC\vartriangle ABC such that BT∥CPBT \parallel CP. Prove that ∠TSC=∠BAC\angle TSC = \angle BAC.
(Anton Trygub)
geometryparallelogramcircumcircleequal angles