Find the eccentricity of the incentre of the triangle PSS'?

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Example 3: A variable point P on the ellipse of eccentricity e, is joined to focii S and S'. Find the eccentricity of the incentre of the triangle PSS'? Support the channel:
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Sir why u chose B as (eb/e+1) raised to power two only why not B as (ae) raised to power two

Ramesh-itkk