| 11. | Twelve key lengths of a triangle are the three side lengths, the three angle bisectors.
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| 12. | The excenter of an ex-tangential quadrilateral lies at the intersection of six angle bisectors.
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| 13. | The perpendicular bisector construction forms a quadrilateral from the perpendicular bisectors of the sides of another quadrilateral.
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| 14. | Construct the perpendicular bisectors to the two segments A 1 A 2 and B 1 B 2.
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| 15. | The excenter ( center of the tangent circle ) lies at the intersection of six angle bisectors.
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| 16. | :I think this occurs for any triangle for any point on one of the angle bisectors.
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| 17. | So the locus for & alpha; = 180?is the union of the three angle bisectors.
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| 18. | In an acute triangle the circumcenter divides the interior perpendicular bisectors of the two shortest sides in equal proportions.
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| 19. | These polygons are made by drawing lines between gauges, then making perpendicular bisectors of those lines form the polygons.
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| 20. | At least two of these bisectors must intersect, and their intersection point is the center of the solution circle.
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