1. **Problem statement:** In a circle with center O, points A, B, C, and D lie on the circumference. Chord AB is drawn and angle ACB is formed at point C on the circle. Given that angle AOB = 100°, find the size of angle ACB and state the circle theorem used. 2. **Relevant theorem:** The angle subtended by a chord at the center of the circle is twice the angle subtended by the same chord at any point on the circumference. Mathematically, if $\angle AOB$ is the central angle and $\angle ACB$ is the inscribed angle subtended by the same chord AB, then: $$\angle AOB = 2 \times \angle ACB$$ 3. **Calculate angle ACB:** Given $\angle AOB = 100^\circ$, use the formula: $$100^\circ = 2 \times \angle ACB$$ Divide both sides by 2: $$\cancel{2} \times \angle ACB = \frac{100^\circ}{\cancel{2}}$$ Simplify: $$\angle ACB = 50^\circ$$ 4. **Answer:** - a) The size of angle ACB is $50^\circ$. - b) The circle theorem used is the "Angle at the center is twice the angle at the circumference" theorem.