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**HallsofIvy** You might also use the fact that if the lines corresponding to $\displaystyle y= m_1x+ b_1$ and $\displaystyle y= m_2 x+ b_2$ are perpendicular, then $\displaystyle m_1m_2= -1$. You know that a radius passing through (4, 8) and (12, 6). What is the slope of that line? You know that the tangent at (12, 6) is perpendicular to that radius so you can find the slope of the tangent. Now you know the slope and one point of the line so you can find the equation of the line.