Question 109
Quadrilateral $ABCD$ and point $T$ in its interior is given such that $AC$ is the angle bisector of $\widehat{BCD}$ and
$$
\widehat{ABC} - \widehat{ATD} = \widehat{DAC}, \quad \widehat{ADC} - \widehat{ATB} = \widehat{BAC}.
$$
Prove that $\widehat{BAT} = \widehat{DAC}$.
$$
\widehat{ABC} - \widehat{ATD} = \widehat{DAC}, \quad \widehat{ADC} - \widehat{ATB} = \widehat{BAC}.
$$
Prove that $\widehat{BAT} = \widehat{DAC}$.