More advanced circle theorems

1. Opposite angles in a cyclic quadrilateral add up to 180°

• Double-check is that all 4 vertices of the quadrilateral are on the circumference
• The diagram below shows a common scenario that is?NOT?a cyclic quadrilateral:

2. The perpendicular bisector of a chord is a radius

• This is also easier to see than remember from its description
• Problems here involve the radii being joined to the end of the chords and so creating two congruent triangles