PAT is tangent to the circumcircle of triangle abc such that pt is parallel to bc. show that ab=ac​

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Please find below the solution to the asked query:

$$\begin{gathered} \Rightarrow \angle \mathrm{PAB}=\angle \mathrm{ABC} \mathrm{and} \angle \mathrm{TAC}=\angle \mathrm{ACB} \mathrm{because} \mathrm{interior} \mathrm{alternate} \mathrm{angles} \mathrm{are} \mathrm{same} \\ \mathrm{And} \\ \Rightarrow \angle \mathrm{TAC}=\angle \mathrm{ABC} \mathrm{and} \angle \mathrm{PAB}=\angle \mathrm{ACB} \mathrm{because} \mathrm{of} \mathrm{alternate} \mathrm{segment} \mathrm{theorem} \\ \mathrm{So} \\ \Rightarrow \angle \mathrm{ABC}=\angle \mathrm{ACB} \\ \mathrm{hence} \mathrm{if} \mathrm{in} \mathrm{a} \mathrm{triangle} \mathrm{two} \mathrm{angles} \mathrm{are} \mathrm{same} \mathrm{so} \mathrm{that} \mathrm{their} \mathrm{opposite} \mathrm{sides} \mathrm{are} \mathrm{same} \\ \mathrm{Hence} \\ \mathrm{AB}=\mathrm{AC} \left(\mathrm{hence} \mathrm{proved}\right) \end{gathered}$$
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