IMC Key Stage 3 · 8. Circles, tangents and inscribed angles
Join the centre to what you know: radii, perpendiculars to chords, inscribed angles, equal tangents and touching circles turn circle problems into right triangles and similar triangles.
IMC Key Stage 3 – Selected topics
Use the perpendicular from the centre to a chord and the angle in a semicircle to compute lengths.
Apply central angles, inscribed angles and cyclic quadrilaterals to find angles.
Solve problems with tangents, circles in corners and touching circles.
Use equal tangent segments, the incircle formulas and Pitot's theorem.
Build similar triangles from the tangent–chord angle and intersecting chords.