O\(\hat{P}\)T = 90º (The radius is perpendicular to the tangent at the point of contact.) Sum of angles in \(\triangle\) PQT = 30 + ( 90 + x ) + (x + 2x) = 180 = 120 + 4x = 180 4x = 180 - 120 = 60º x = \(\frac{60}{4}\) = 15^\circ Therefore, P\(\hat{T}\)O = 2x = 2 x 15 = 30º