To solve geometry problems about circles, you will need to know the following circle theorems involving tangents, secants, and chords. These theorems can be used to find information about angles, intercepted arcs, and length of segments of a circle. In addition, you find the standard and general form of a circle, the formulas for area and circumference, and the area of a sector of a circle.
Circle formulas
The circumference of a circle equals
The area of a circle equals
The area of a sector equals
Standard form of a circle:
General form of a circle:
Circle theorems involving angles
The central angle equals the intercepted arc.
An inscribed angle equals
The interior vertical angles formed by two intersecting chords equal
An exterior angle equals
A line tangent to a circle is perpendicular to the radius drawn to the point of tangency.
Circle theorems involving lengths of segments
When a tangent and secant are drawn from the same exterior point,
When two secants are drawn from the same exterior point,
