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In parallelogram EFGH, let M be the point on EF such that FM:ME = 3:5 and let N be the point on EH such that HN:NE = 2:5.  Line segments FH and GM intersect at P, and line segments FH and GN intersect at Q.  Find PQ/FH.

 Mar 24, 2024
 #1
avatar+128406 
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PQ / FH  

Triangle HQN  similar to triangle FQG          Triangle MPF  similar to triangle GPH

HQ / HN  = FQ / FG                                       MF / PF = GH / PH                    

HQ / 2  =  FQ / 7                                            3 / PF = 8 / PH                                        

HQ/FQ = 2/7                                                  PF / PH= 3/8

 

HQ = (2/9)FH   

PF = ( 3/11)FH

 

HQ = (22/99)FH

FP  = (37/99)FH

PQ = [ 99 - 22 - 27 ] / 99 = 50/99 FH

PQ / FH   = 50 / 99

 

cool cool cool                                                        

 Mar 24, 2024

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