ABC is a triangle and R any point on the segment AB. Let P be the intersection of the line BC and the line through A parallel to CR. Let Q be the intersection of the line AC and the line through B parallel to CR. Show that 1/AP + 1/BQ = 1/CR.
Solution
By similar triangles, CR/AP = BC/BP and CR/BQ = AC/AQ = CP/BP. Hence CR/AP + CR/BQ = 1.
© John Scholes
jscholes@kalva.demon.co.uk
29 Oct 2003
Last corrected/updated 29 Oct 03