MathDB
AD = CD wanted, tangents to circumcircle (2011 Kyiv City MO 9.4.1)

Source:

July 14, 2020
geometrycircumcircleTangentsequal segments

Problem Statement

The triangle ABCABC is inscribed in a circle. At points AA and BB are tangents to this circle, which intersect at point TT. A line drawn through the point TT parallel to the side ACAC intersects the side BCBC at the point DD. Prove that AD=CDAD = CD.