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Infographic Geometry Problem 1056: Triangle, Exradius, Reciprocals of the Altitudes, Multiplicative Inverse, Perpendicular, Excircle, Circle, Tangent. Level: High School, College, Mathematics Education

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In a triangle ABC with the altitudes ha, hb, and hc and the exradii ra, rb, rc, prove that: 1/ra = 1/hb + 1/hc - 1/ha, similarly, 1/rb = 1/ha + 1/hc - 1/hb, and 1/rc = 1/ha + 1/hb - 1/hc. (See the figure below)

 

Geometry problem 1056: Triangle, Exradius, Reciprocals of the Altitudes, Multiplicative Inverse, Perpendicular, Excircle, Circle
 
 


 

 

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1051-1060 | Triangle | Altitude | Perpendicular lines | Circle | Exradius | Circle Tangent Line | Problem 1071 | Problem 764 | Problem 195  | Email | Solution / comment | by Antonio Gutierrez
Last updated: Nov 6, 2014