In the above figure, AB∥MN∥PC, then which of the following will be true?
1AB+1PC=1MN
In △ MNC and △ ABC
∠ MNC=∠ ABC=90∘
∠ MCN=∠ ACB(common angle)
Therefore, △ MNC∼△ ABC by AA similarity
So, MNAB=NCBC ---- I
In △ MNB and △ PCB
∠ MNB=∠ PCB=90∘
∠ MBN=∠ PBC (common angle)
Therefore, △ MNB∼△ PCB by AA similarity.
So, MNPC=BNBC --- II
Adding I and II,
MNAB+MNPC=NCBC+BNBC
MN [1AB+1PC]=BCBC
⇒1AB+1PC=1MN