Dynamic Geometry: P88

The diagram shows a black semicircle. A red point moves freely on its diameter, creating a green and a cyan semicircle. The pink semicircle is internally tangent to the black semicircle and tangent to both bottom semicircles. The purple and orange semicircles are tangent to the pink semicircle and to one of the bottom semicircles. When the ratio of the purple circle to the radius of the orange is equal to $\dfrac{49}{155}$ , the ratio of the blue semicircle's radius to the radius of the green semicircle can be expressed as $\dfrac{p}{q}$ , where $p$ and $q$ are coprime positive integers. Find $p+q$ .