Drag the green dots around to see the theorems and equations at work.
A) Place the point P inside of the circle. What is the product of the two pieces of the pink line segment? What is the product of the two pieces of blue segment? [br]
B) Place the point P outside of the circle. What is the distance from P to the green point on the pink line? From P to the blue point on the pink line?. What is the product of those two lengths? What is the distance from P to the green point on the blue line? From P to the blue point on the blue line?. What is the product of those two lengths?[br][br]C) Place the point P outside of the circle so the pink segment does not go into the circle (the green dot matches with the blue dot). [br]i) What is the distance from P to the green point on the blue line? From P to the blue point on the blue line?. What is the product of those two lengths?[br]ii) What is the distance from P to the green point on the pink line? From P to the blue point on the pink line?. What is the product of those two lengths?[br][br]D) Did you expect these relationships? Why or why not?[br][br]E) State the theorem in your own words.
A) What is the difference between the measure of Arc 1 and Arc 2? What is half of that value?[br][br]B) How does that number compare to the value of angle P? Does that surprise you? Why or why not?[br][br]C) State this theorem in your own words.