A triangle with a cevian. Two lengths are given. What length is x?

Scroll down for a solution to this problem.

## Solution

The length x is 1.

This is a typical application of similarity. Triangle ADC is similar to triangle EAC because all three angles are equal. Therefore (x+3)/2=2/x. This gives can be rewritten as (x+4)(x-1)=0. Since x is positive, it must be 1.

## Poem

Like big wings of a butterfly

A nice show in the sky

And wind and sun from july

The pilot skydives and flies

As beautiful as seagulls trumpeting by

We love him, we don’t know why

He makes the run with so much grace

He kisses the heaven high

With our dreams, they never dy.