3. Given a cyclic quadrilateral $ABCD$ satisfying $AB=BC=AD+CD, \angle BAD=\alpha, AC=d$. Find the area of $\triangle ABC$.

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The translation maintains the original format and line breaks as requested.
$$
\begin{array}{l}
\text { So } B O=A C=d \\
\text { So } S_{\triangle A B C}=S_{\triangle A B O}+S_{\triangle O B C} \\
=\frac{1}{2} A O \cdot B O \cdot \sin \angle A O B+\frac{1}{2} O C \cdot B O \cdot \sin \angle B O C \\
=\frac{1}{2} A C \cdot B C \cdot \sin \alpha \\
=\frac{1}{2} d^{2} \sin \alpha \\
\end{array}
$$

That is, $S_{\triangle A B C}=\frac{1}{2} d^{2} \sin \alpha$