SMO Open · 10. Circles, tangents and cyclic quadrilaterals
Angles and lengths in circles: inscribed angles and cyclic quadrilaterals, the arc midpoint and chord lengths, tangents and the circles hidden behind right angles, the power of a point and the radical axis, with a Round 2 proof.
Use inscribed angles, arcs and cyclic quadrilaterals to find angles.
Use the arc midpoint lemma and the chord formula $2R\sin\theta$.
Use tangent properties and find circles with a diameter from right angles.
Apply the power of a point and the radical axis to compute lengths.
Write a short proof combining Pythagoras and the power of a point.