Chapter: Circle· Mathematics Part 2 (Geometry)
Answer: \(m\angle ACB = 65^\circ\), m(arc AB) = 130°
By the tangent secant angle theorem, the angle between a tangent and a chord through the point of contact is half the intercepted arc: \(65^\circ = \dfrac{1}{2} m(\text{arc AB})\) \(\therefore m(\text{arc AB}) = 130^\circ\).
\(\angle ACB\) is inscribed in the other arc and intercepts the same arc AB, so \(m\angle ACB = \dfrac{1}{2} \times 130^\circ = 65^\circ\) (angle in the alternate segment equals the tangent-chord angle).