Lista de exercícios do ensino médio para impressão

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The circle as shown in the picture below, with center P and radius 2, is tangent to three sides of the rectangle ABCD. Given that the total area of the rectangle is 32, find the distance between the point P and the diagonal AC.

a)

$\,2\dfrac{\sqrt{5}}{5}\,$

b)

$\,\dfrac{\sqrt{5}}{2}\,$

c)

$\,\dfrac{\sqrt{5}}{5}\,$

d)

$\,2\sqrt{5}\,$

e)

$\,3\dfrac{\sqrt{5}}{5}\,$