A TANGENT and a RADIUS meet at 90 DEGREES.
2 RADII form an ISOSCELES TRIANGLE.
The PERPENDICULAR BISECTOR of a CHORD passes through the CIRCLE'S CENTRE.
(perpendicular means it meets at 90 degrees)
The ANGLE AT THE CENTRE of a circle is 2X the ANGLE AT THE CIRCUMFERENCE.
The ANGLE in a SEMI-CIRCLE is 90 DEGREES.
This is because the angle at the centre of the circle is 180 degrees.
OPPOSITE ANGLES in a CYCLIC QUADRILATERAL add up to 180 DEGREES.
TANGENTS from the SAME POINT are EQUAL IN LENGTH.
From this, two congruent right-angled triangles can be made...
Rule 9 (FINAL ONE!)
THE ALTERNATE SEGMENT THEOROM...
The ANGLE BETWEEN a TANGENT and CHORD is EQUAL to that of an ANGLE made from the cord in the OPPOSITE SEGMENT.