Circle Theorems

主题:角

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.

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