Circle Theorums

Circle Theorums

1. An inscribed angle is an angle made from two points on the circles circumference

   • an inscribed angle is half the corresponding central angle subtended on the same arc
     • two inscribed angles subtended on the same arc are equal, this looks kinda like butterfly wings

2. An angle inscribed (touching the circumference) in a semicircle is always a right angle

   • If you reflect the triangle on the other side of the diameter, you get a reactangle, all angles in a rectangle are 90 degrees so it's 90 degrees

3. A cyclic quadralateral must touch the circumference with every side

   • The opposite angles in a cyclic quadralateral add up to 180 degrees

4. A tangent always forms a right angle with the circle's radius

   • The exterior angle between a triangle and a tangent that are touching is equal to the opposite interior angle of the triangle. for instance, the angle on the left of a triangle and the tangent is the same as the angle in the top right of the triangle
     • The angle between the tangent and the diameter is 90 degrees, therefore angle OAC is 90 - x. Angle C is 90 degrees as it is in a semicircle, and the angles in a triangle add up to 180 so OAC is 180 - 90 - y or 90 - y, so OAC is 90 - y and 90 - x meaning x = y

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