A quadrilateral $ABCD$ is inscribed in a circle and the lenght of side $AD$ equals the sum of the lenghts of the sides $AB$ and $CD$. Prove that the angle bisectors of $\angle ABC$ and $\angle BCD$ meet on the side $AD$.
Source: Brazil Cono Sur TST 2023 - T3/P1
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A quadrilateral $ABCD$ is inscribed in a circle and the lenght of side $AD$ equals the sum of the lenghts of the sides $AB$ and $CD$. Prove that the angle bisectors of $\angle ABC$ and $\angle BCD$ meet on the side $AD$.
