Mathematics
In the adjoining figure, in △ABC, O is any point in its interior. Show that: OB + OC < AB + AC
Answer
We know that,
In a triangle, sum of any two sides is always greater than the third side.
In △ABD,
⇒ AB + AD > BD
⇒ AB + AD > OB + OD …..(1)
In △COD,
⇒ OD + DC > OC …..(2)
Adding eq.(1) and (2), we have:
⇒ AB + AD + OD + DC > OB + OD + OC
⇒ AB + (AD + DC) > OB + OC
⇒ AB + AC > OB + OC
⇒ OB + OC < AB + AC.
Hence, proved that OB + OC < AB + AC.
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