Passel of Techniques -- 2

Geometry Level 4

Let \(ABC\) be a triangle in which \(AB = AC\). Suppose the orthocenter of the triangle lies on the incircle, find the ratio \( \dfrac{ AB }{ BC }\).

If this ratio can be expressed as \( \frac pq\), where \( p\) and \(q\) are coprime positive integers, submit your answer as \(p+ q\).

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