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
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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