Math, asked by ayushbiswas1000, 5 months ago

ABC is any triangle. D is any point on BC. Join AD ; At B and C, BR and CT are drawn

parallel to AD ; BA and CA are produced to meet the parallel lines at T and R respectively. Prove that 1/ AD = 1/RB +1/TC​

Answers

Answered by amitnrw
1

Given :  ABC is any triangle. D is any point on BC. Join AD ;

At B and C, BR and CT are drawn parallel to AD ;

BA and CA are produced to meet the parallel lines at T and R respectively.

To Find :  Prove that 1/AD = 1/RB + 1/TC

Solution:

RB || AD  

Hence ΔACD ~ Δ RCB

=> AD/RB =   CD/CB    Eq1

CT || AD  

Hence ΔABD ~ Δ TBC

=> AD/TC = BD/CB     Eq2

Eq1 + Eq2

=>  AD/RB  + AD/TC  =  CD/CB  + BD/CB

=> AD/RB  + AD/TC  =  (CD + DB)/CB  

=> AD/RB  + AD/TC  =  (CB)/CB  

=> AD/RB  + AD/TC  =  1

Dividing both sides by AD

=> 1/RB + 1/TC   = 1/AD

QED

Hence proved

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