Explorations in Geometry

with the

Geometer’s Sketchpad

Exploration 9

- Construct a Circle O, and three points A, B, & C on the circle to form triangle ABC.
- Find the midpoints of the three segments of the triangle, and measure the distance from the center of the circle to the three midpoints (I show the segments above as x, y, and z.
- Can you find a relationship between the lengths of segments x, y, and z and the triangle ABC. (hint, you will need to measure the angles )
- What happens when the triangle is obtuse?
- What other geometric or algebraic relationships can you find in this figure?
- Write a brief paragraph explaining what you have found in this exploration. Remember to answer all the specific questions above.