A. B and C are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 13 - 2018 - Paper 1

To find angle CAO, we can use the relationship of angles at the circumference and properties of tangents.

1. Identify Angles: We know two angles:

   • Angle BAE = 56°
   • Angle CBO = 35°

2. Determine angle AOB: Angle AOB forms the angle at the center over the arc AB, which is equal to twice the angle at the circumference. Thus, $\text{Angle AOB} = 2 \times \text{Angle BAE} = 2 \times 56° = 112°$

3. Calculate angle AOC: The angles in triangle AOC can be summed up to 180°: $\text{Angle AOC} = 180° - \text{Angle CBO} - \text{Angle AOB}$ Substituting the known values: $\text{Angle AOC} = 180° - 35° - 112° = 33°$

4. Use Angle CAO: The angle CAO, being a part of triangle AOC, can be related through the exterior angle theorem. Thus, $\text{Angle CAO} = \text{Angle BAE} - \text{Angle AOC} = 56° - 33° = 23°$

Therefore, the size of angle CAO is 23°.