A google and amazon interview question with a really clever solution

The video explores the probability of forming a triangle by randomly cutting a stick at two points. It introduces Viviani's theorem, which states that the sum of perpendicular distances from any interior point to the sides of an equilateral triangle equals the triangle's height. This theorem is applied to the stick problem, showing that only one of four possible regions allows for a triangle to be formed, resulting in a 25% probability. The video concludes with a practical application of this geometric concept.

Explain Viviani's theorem and its significance in the context of triangle formation.

What is the condition for three pieces to form a triangle?

How does the interior point relate to the cuts made on the stick?

What happens when the two shorter sides of a triangle do not exceed the length of the third side?

What is the probability of randomly cutting a stick into three pieces that can form a triangle?