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Thread: Math Question (Geometry).. Please Help

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    Math Question (Geometry).. Please Help

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    A circle is inscribed in an equilateral triangle. Radii to two of the points of tangency are shown. What is x?
    The answer given is 240 degrees. The explanation states that "the radii are two sides of a quadrilateral. A line tangent to a circle meets a radius at the point of tangency at 90 degree angle. Each angle of the equilateral triangle is 60 degrees. Therefore, the remaining angle of the quadrilateral measures 120 degrees. A circle has 360 degrees. So, the measure of angle x can be found using subtraction: 360-120=240.
    I don't understand how this figure is a quadrilateral. I also don't understand how the 90 degree angle fits into the solution to the problem.
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    GRE-GMAT Instructor Brent Hanneson's Avatar
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    Re: Math Question (Geometry).. Please Help

    Here's another approach:
    Draw a 3rd line from the center to the bottom point of tangency (where the triangle side touches the circle).
    This divides the circle into 3 equal sectors (pieces of pie).
    360/3 = 120, so each sector has an angle of 120 degrees at the center.
    So, the unlabeled angle in the diagram = 120 degrees, which makes angle x = 240 degrees.

    Cheers,
    Brent

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