Question

P is a point on side BC of a triangle ABC prove that AB
+ BC + AC greater than 2 AP

Answer 1

In triangle ABP

AB+ BP > AP…….(1)

In triangle ACP

AP + CP > AP…….(2)

By adding the equation 1 & 2 we get

AB + AC +( BP+CP) > 2AP

where BP +CP = BC ( acc. to figure)

Hence …. AB + BC + CA > 2 AP

PROVED………..
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Answer 2

Question:

P is any point inside the triangle ABC. let's prove that, (i) AP+BP>AB (ii) AB +BC +AC <2(AP +BP +CP ).