The hawfinch

An equilateral triangle with a circle tangent to two sides. The vertices are the tangency points. What is the length proportion of line segments x : y?

Scroll down for a solution to this problem.


The proportion x : y is 1 : 2.

Solution by Matthew Arcus using Stewart’s Theorem.


The hawfinch
A harmless quiet little bird
So grey and brown
He sings a quiet tune
A nice chirping sound
In the evening trees
In the bright sky so blue
He flies
With his little wings
In the nature around
Looking for a shelter
And a place to rest
Where he builds a cosy nest


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