# Jewellers problem

**Geometry**Level 4

A Jeweller wants to maximize the area of a triangular emerald within his earring. He uses three touching circles as a geometrical model of the earring.

If the radius of all three circles is **12**, what is the maximum possible area of the triangle that fits within the red region?

Give answers to one decimal place.

Bonus: Can you prove that your answer is a maximum?