What 3 geometry theorems are dynamically being illustrated in the applet below?
You can actually only view 1 theorem at a time.
To see a theorem other than the one currently being seen here, move any 1 (or more) pink points as far up or down the circle as you possibly can.
(Feel free to move any point anywhere you'd like at any time!)
Theorem:
The measure of an angle formed by 2 secant rays drawn to a circle from a point outside the circle is equal to half the difference of the measures of their intercepted arcs. (The pink arc and the green arc are the intercepted arcs.)
Other theorems:
Simply replace the phrase "angle formed by 2 secant rays" in the theorem above with the phrase "angle formed by a secant ray and a tangent ray" or "angle formed by 2 tangent rays". (These theorems can be seen by moving one or both pink points as far up or down as they can go on the circle.)
Recall that an inscribed angle of a circle measures half its intercepted arc. Hence, "half the pink arc" minus "half the green arc" equals the measure of the blue angle.
