SMO Junior · 10. Circles, tangents and inscribed angles
Right triangles from chords, equal tangents and incircles, right angles from diameters and inscribed angles, and the tangent–chord angle in proofs.
Compute radii, chords and distances with the centre – midpoint – endpoint right triangle.
Use tangent properties, incircles and touching circles.
Use inscribed angles, angles in a semicircle and cyclic quadrilaterals.
Find areas of regions built from sectors, semicircles and triangles.
Write short geometry proofs using the tangent–chord angle.