89 
A New TRIANGLE AND Some oF Its Properties. By Ropert Jupson ALEY. 
Explanation of Figure. — ABC is any triangle, of which M is the circum- 
center, O the incenter, H the orthocenter, and @ Nagel’s Point. A’A’”’, B’ B’’” 
and C’C’” are diameters perpendicular to the sides BC, CA, AB, respectively. 
ENA lp 
. 
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I. If AY, BY, CY are the middle points of AA’, BB’, CC’, respectively, 
then OM is the diameter of the cireumcircle of AY BY CY. 
Since AY is the middle point of AA’, 
MAVY is parallel to AA’”’, 
But AA’” is perpendicular to AA’, 
.. MAY is perpendicular to 4A’. 
