Tangent Secant Theorem

The simulation shows a circle and a point P outside it. PT is the tangent to the circle at T, and PAB is a secant, where A and B lie on the circle.

Things to Explore

  1. Drag the point P and observe the expressions PA x PB and PT².
  2. Drag the point A and observe the expressions PA x PB and PT².

Questions

  1. As you drag P, do PA x PB and PT² remain equal?
  2. As you drag A, do PA x PB and PT² remain equal?

That’s all for this exploration. Hope you’ve discovered the relation between the lengths of the tangent and secant to a circle from the same point outside it. Think about how you can formally prove what you discovered.

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