Circle Theorems
Intro to Circle Theorems
Part #1:
For any angle in a triangle above the radius, the angle that touches the surface of the circle has to equal 90°.
In this example, the angle will equal 90° as long as it is above the CB radius.
Move the point D along circle surface to check.
Part #2:
Inscribed Angle Theorems:
An inscribed angle a° is half of the central angle 2a°
Here we have the angle is half of the central angle . Even if you moved the point 
along the circle between the points B and D, you would still get that the angle 
is twice
Move the point C along circle surface to check.
along the circle between the points B and D, you would still get that the angle is twice
Move the point C along circle surface to check.Part #3:
Angles Subtended by Same Arc Theorem:
Notice that the angle C equals the angle E. This Theorem states that these two angles will always be equal to each other as long as they are in the range from B to D
Move the point C and E along circle surface to check.
Part #4:
Cyclic Quadrilateral
A Cyclic Quadrilateral has every vertex on a circle's circumference:
A Cyclic Quadrilateral opposite angles add to 180°.
In this example we have +=180°
And +=180°
Move the points along circle surface to check.