A lot of tangency points

Geometry Level 4

The triangle ABCABC is inscribed in the circle C\mathcal{C}. Circle C1\mathcal{C}_1 is tangent to the minor arc ABAB of C\mathcal{C} and to side ACAC at point PP. Circle C2\mathcal{C}_2 is tangent to the minor arc CBCB of C\mathcal{C} and to side ACAC at point QQ. From point BB draw the tangents BRBR and BSBS to circles C1\mathcal{C}_1 and C2\mathcal{C}_2, respectively. It is known that BA=22BA=22, BC=23BC=23, BR=16BR=16, BS=17BS=17, PQ=15PQ=15. ACAC can be written as ab \frac{a}{b} , where aa and bb are coprime positive integers. What is the value of a+ba+b?

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