Theorems about Tangents & Chords - play around with each of these applets to discover!

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  1. Applet 1 (.ggb)
     
  2. The angle where the radius intersects a tangent line is ALWAYS a right angle (90-degrees!). Try moving the center around and see what happens. You can also move the other points, as well! (.ggb)
     
  3. Applet 3 (.ggb)
     
  4. "Party Hat" Theorem: If TWO tangent lines are drawn from the SAME external point (point C, here), then their tangent SEGMENTS will ALWAYS be congruent! (.ggb)
     
  5. If two chords, AB & CD, are equidistant to the center of a circle (i.e. their 'apothems' are the same length), then the chords, themselves, will ALWAYS be congruent! Don't forget to click on (.ggb)
     
  6. The inscribed angles (
     
  7. The inscribed angles (
     
  8. Applet 8 (.ggb)
     
  9. A Deeper Look: If two chords are congruent, then their intercepted arcs are congruent. (.ggb)
     
  10. If a diameter (EF, here) is perpendicular to a chord (CD, here), then it BISECTS the chord AND it's INTERCEPTED ARC (arc CD will also be bisected).! (.ggb)