The circle below is centred at 0. a) What is the size of angle x? b) Which of the circle theorems below allows you to work out this angle? o x Not drawn accurately Opposite angles in a cyclic quadrilateral add up to 180^circ The angle at the circumference in a semicircle is a right angle Two tangents that meet at a point are the same length The angle between the tangent and the radius at a point on a circle is 90^circ The perpendicular line from the centre of a circle to a chord bisects the chord

the question doesn't provide a diagram or measurements I'm – unfortunately – unable to give an answer to a) or b) regarding what radius "x" would be or which theorem could be used to work it out. However, I can provide explanations for the theorems mentioned:1. When the opposite angles of a quadrilateral inscribed in a circle are added, they always add up to . This is based on the properties of cyclic quadrilaterals.2. The theorem about right angles in semicircle states that if an angle is inscribed in a semicircle, it is right said to be a right one, specifically .3. If you draw two tangents to a circle starting from a point, those two tangents will always be the same length. This is proven using similar triangles in a method beyond the scope of this question.4. At each point on a circle, the tangent line always makes a angle with the radius line that comes from the centre to that point.5. For a chord (a segment connecting two points on the circumference of a circle), a perpendicular line from the center of the circle will bisect (cut in half) the chord, this kind of symmetry is one of the defining properties of the circle.Please let me know if you have more precise measurement data for the specific circle, or if you want me to explain another mathematical concept. It's my pleasure to assist you to understand.