Pedal Triangle!

Geometry Level pending

With usual notations consider that X , Y , Z are the ex-centres of triangle ABC. If the ratio of circumradius of triangle XYZ to the circumradius of $$pedal~triangle$$ of triangle ABC is k : 1 , then what is the value of 'k' ?????

Note : A $$pedal~triangle$$ is a triangle obtained by projecting a point onto the sides of a triangle !!!!!

Enjoy !!!!!

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