SMO Senior · 10. Circles, tangents and cyclic quadrilaterals
Turn angles into arcs, use tangents, the power of a point and Ptolemy's theorem, and handle two touching circles — with full proofs for Round 2.
Compute angles with central, inscribed, tangent–chord and chord–chord angle rules.
Use tangent ⊥ radius and equal tangent segments to find lengths and perimeters.
Apply the power of a point for chords, secants and tangents.
Recognise cyclic quadrilaterals and apply Ptolemy's theorem correctly.
Write a complete proof about two touching circles using angle chasing.