**Problem 1.**

Let a, b, c be positive numbers such that

and .

Prove that there exists a triangle with side lengths a, b and c.

**Problem 2.**

Consider the inequality

where a, b, c are the side lengths of a triangle and k is a real number.

(a) Prove the inequality when .

(b) Find the least value of k such that the inequality holds true for any triangle.

**Problem 3.**

Let a, b, c be positive real numbers. Prove that they are side lengths of a triangle if and only if

for any real numbers p, q, and r such that and .

*Let me know if you **need any help when you attempt it..*

Nalin Pithwa