I found this the other day online, and its fairly interesting:
a circle is inscribed in a 36 degree sector of a circle with an area of 25(pi) cm squared. What is the circumfrance and area of the smaller circle?
I'm having some trouble wrapping my head around it though. any help?
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Some construction is necessary.Draw a tangent at the point that the sector chords perpendicular bisector meets both circles.Extend the two radii to meet this tangent.This creats two isosceles triangles.Draw the chord of one 18 deg sector.Do you see how to proceed starting with 1/2 of 3.1 to find 1/2 the base of the larger isosceles triangle from which the radius of the small circle is calculated from 36 deg rt triangle. center of small circle lies on the intersection of two angle bisectors of the large triangle