Τρίτη, 20 Ιουλίου 2010

THREE CONCURRENT CIRCLES


5. Let 123 be a triangle, 4 a point inside 123 and (1') the circle touching the circles (134), (124) externally and the circle (234) internally at 5, (2') the circle touching the circles (214),(234) externally and the circle (314) internally at 6 and (3') the circle touching the circles (324),(314) externally and the circle (124) internally at 7.

The circles (167),(275),(356) concur at a point 8.

Variation:


Let (0) be the circle touching internally the circles (234), (314), (124) at 5,6,7 resp.


The circles (167),(275),(356) concur at a point 8.

Note:


If 4 is not inside triangle 123, but in the negative side of 23 (ie the side not containing 1), then (1') is the circle touching (314),(124) internally and (234) externally at 5.

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