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