Surface area of earth not covered by satellite revolving around the earth orbit

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A remote sensing satellite is revolving in an orbit of radius x over the equator of earth . Find the area on earth surface in which satelllite can not send message?

Radius of earth R, equitorial distance of satellite is x.

I arrived at answer of $4\pi R^2 [1- {(x-R)\over 2x}]$. However the book answer is $4\pi R^2 [1- {\sqrt{x^2-R^2}\over x}]$. Help me out here.