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Nine point circle (Posted on 2024-11-23) Difficulty: 3 of 5
Two circles U and V with radii 32 and 12, respectively, have centers 16 units apart. Find the length of the curve determined by the set of the centroid (intersection of the medians) of all triangles with U as their circumcircle and V as their inscribed circle.

No Solution Yet Submitted by Danish Ahmed Khan    
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First thought Comment 1 of 1
I decided to add the nine point circle.  It appears the center of this circle itself traces out a circle.

This new circle is a dilation (mag 3/2 centered at the large circle) of the one sought.

https://www.desmos.com/geometry/y1yzajg1q7


Edited on November 23, 2024, 5:54 pm
  Posted by Jer on 2024-11-23 17:37:48

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