how am i supposed to solve the line perpendicular to the tangent line when i have two unknowns (the coordinates at the center and the end of the circle)
how am i supposed to solve the line perpendicular to the tangent line when i have two unknowns (the coordinates at the center and the end of the circle)
You are not supposed to do that.
You know that $\displaystyle 2p+3q=4$ because it is on the line.
The distance formula gives you $\displaystyle \frac{|2p+q-3|}{\sqrt{2^2+1^2}}=\sqrt{5}$.