# Circumcenter (& Questions)

Recall that 3 or more lines are said to be concurrent if and only if they intersect at exactly 1 point. A triangle's 3 perpendicular bisectors are concurrent. Their point of concurrency is called the CIRCUMCENTER of the triangle. In the applet below, point C is the circumcenter of the triangle. Move the white vertices of the triangle around and then use your observations to answer the questions that appear below the applet.
Questions: 1) Is it ever possible for a triangle's circumcenter to lie OUTSIDE the triangle? If so, under what circumstance(s) will this occur? 2) Is it ever possible for a triangle's circumcenter to lie ON THE TRIANGLE ITSELF? If so, under what circumstance(s) will this occur? 3) If your answer for (2) was "YES", where on the triangle did point C lie? 4) Is it ever possible for a triangle's circumcenter to lie INSIDE the triangle? If so, under what circumstance(s) will this occur? 5) Now, on the applet above, construct a circle centered at C that passes through J. What do you notice? (Hint: Look at points K & L.) 6) Let's generalize: The circumcenter of a triangle is the ONLY POINT that is.............(If you need a hint to complete this step, consider the lengths CK & CL with respect to length CJ.) 7) Take a look back the worksheet found here﻿. Use your observations from examining this worksheet again to explain why the phenomenon you observed in step (5) and your response to this phenomenon (in step 6) occurred.