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Math: Geometry Problem 1023: Triangle, Contact, Gergonne, Product of three distances. Level: School, College.

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In the figure below, P is a point on the incircle of triangle ABC and TATBTC is the contact triangle. If PA1, PB1, PC1, PA2, PB2, and PC2 are perpendicular to BC, AC, AB, TBTC, TATC, and TATB, respectively, Prove that
PA1.PB1.PC1 = PA2.PB2.PC2.
 
The contact triangle or intouch triangle or Gergonne triangle of a triangle ABC is defined by the 3 tangency points of the incircle on the 3 sides.

Geometry Problem 1023: Triangle, Contact, Gergonne, Product of three distances

 


 

 

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Last updated: Sep 19, 2014