Question 5
Circle $\left(O\right)$ has diameter $AB$ and $C$ lies on $AB$. Circles with diameters $AC , CB$ have tangent lengths $ME , MF$ from $M$ on $\left(O\right) , M \ne A , B$. $a$)Prove $\left(\frac{ME}{MA}\right)^{2} + \left(\frac{MF}{MB}\right)^{2} = 1$. $b$)Find $C$ such that $ME = \frac{MA}{2}$.