Circle Inscribed in SectorDate: 05/20/99 at 17:38:29 From: Chris Wipke Subject: Geometry The arc of a sector has degree measure 60 degrees. The radius of the sector is 12 inches. Find the area of the circle that can be inscribed in the sector. I have drawn a diagram of a sector whose arc measure is 60 degrees, and have constructed a line perpendicular to the lower segment forming the arc. I do not know what to do from here, or if I am right so far. Please provide me the way to figure out the problem, along with the correct answer. Date: 05/21/99 at 13:04:25 From: Doctor Peterson Subject: Re: Geometry Hi, Chris. Interesting problem! Here's how I understand your picture: ** / **** / +++++** +++ +++ + *+ + + + /+ +* / + + * /60 +++ +++ * *---------+++++-------* 12 I would draw in a couple lines: a radius from the center of the inscribed circle to its point of tangency with a radius of the sector, and a radius of the sector passing through the center of the inscribed circle. A ** / **** / +++++** C +++ +++ + D /r *+ + + + /+ / | +* / +/ |r + * / / +++ | +++ * *---------+++++-------* O E B Now because the circle is tangent to the arc, OC is a radius of the arc and has length 12. OD, the hypotenuse of a right triangle, has length 12-r. But triangle ODE is a 30-60-90 triangle, so we know this hypotenuse is exactly twice r. This will give you an equation you can solve for r. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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