Angles of a Circle
Inscribed angle
Section titled “Inscribed angle”An inscribed angle has its vertex on the circumference of a circle. Inscribed angles that subtend the same arc are equal.
Central angle
Section titled “Central angle”A central angle has its vertex at the center of the circle. A central angle subtending a given arc is twice the inscribed angle subtending the same arc.
Thales’ theorem
Section titled “Thales’ theorem”Thales’ theorem states that an angle inscribed in a semicircle is a right angle. In other words, a triangle that has a diameter as one side is always a right triangle.
Proof of the inscribed angle theorem
Section titled “Proof of the inscribed angle theorem”The inscribed angle theorem states that inscribed angles subtending the same arc are equal and are half the measure of the corresponding central angle.
This can be proved using the triangle property that an exterior angle equals the sum of the two opposite interior angles.