A regular pentagon ABCDE is inscribed in a circle as shown.

Write a formula for the area of the smaller circle inscribed in BCD in terms of r_{1}, the radius of the larger circle.

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Area of small circle = pi * (0.38197*r1) ^ 2

not quite ðŸ™‚

Quite close though.

It’s late and I should check but I think it is

area = pi * (0.309017*r1) ^ 2

0.309.. = (cos (18) * sin(3*18) (1- sin (18)))/(sin (4* 18)+cos(18)sin(3*18))

Used sine rule and a congruent triangle and a few other obv things

0.309= sin18, but yes, you’re correct ðŸ™‚