A Concurrency from the Midpoints of Line Segments through the Circumcenter

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Let ABC be a triangle with circumcenter O. Let A', B', and C' be the perpendicular projections of A, B, and C onto BC, CA, and AB, respectively. Let
D=AO⋂BC
,
E=BO⋂AC
, and
F=CO⋂AB
. Let A'', B'', and C'' be the midpoints of AD, BE, and CF, respectively. Then A'A'', B'B'', and C'C'' are concurrent.

External Links

Circumcenter (Wolfram MathWorld)
Circumcircle (Wolfram MathWorld)
Concurrent (Wolfram MathWorld)
Midpoint (Wolfram MathWorld)

Permanent Citation

Jay Warendorff
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​"A Concurrency from the Midpoints of Line Segments through the Circumcenter"​
​http://demonstrations.wolfram.com/AConcurrencyFromTheMidpointsOfLineSegmentsThroughTheCircumce/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011