#3.7

Aim: to use knowledge of incenter and circumcenter to solve problems

• (1-13) omit #6

Mack Daddy Construction

Aim: to use knowledge of constructions to discover which 3 centers (incenter, circumcenter, orthocenter, centroid) are collinear

• draw a medium-large acute scalene triangle
• construct the incenter (I recommend highlighting this incenter with a particular color, say pink, for instance.)
• construct the circumcenter (I recommend highlighting the circumcenter with a different color than the incenter, perhaps blue.)
• construct the orthocenter (I recommend highlighting the orthocenter with different colors than the incenter and circumcenter, green anyone?).
• construct the centroid (I recommend highlighting the centroid with a fourth and final color than you used for the first 3. How about yellow?).
• 3 out of the 4 centers will be collinear. If you use highlighters as I suggested, then 3 of your colors should line up.
• Your mission, should you choose to accept it (not like you actually have a choice though if you want pass Ch. 3), is to tell me which 3 centers are collinear.
• You might have to do this mack daddy construction several times. that's okay. Practice makes more perfect constructions anyway.
• Some of the best of all time (Mary, Mary, quite contrary) had to do it 6 times before she was able to discern which 3 centers are collinear.
• And IF, by some strange reason, you should have some extra time to practice, I would strongly advise that you practice inscribing a circle in an obtuse triangle AND circumscribing a circle about an obtuse triangle!