Triangle in a circle

Show this first animation and ask, what do you notice?  What do you wonder?

Then ask the following:  If the diameter of the circle is 8 cm.  What (or when) is the largest area?  What are the dimensions of this triangle? 

After students solve that pose, When is the area exactly half the largest?  What are the dimensions of that triangle?  What is the angle?


After some work time and playing around with the above problem, show them this animated version

Trig Ratios animated

Two different triangles are animated.  Show your class this animation and simply ask:

• What do you notice?
• What do you wonder?

After some conversations show them this one, with the side lengths being shown and ask again:

• What do you notice?
• What do you wonder?

Lastly, show them this image and ask them "How could we analyze this?"

  Some possible routes:

• Prove the sides hold true for Pythagorean theorem
• What angle(s) would be in the triangle?
• How are these 2 triangles similar?  How are they different?