Please help with a trapezoid - circle problem

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A circle with radius 3 is inscribed in a isosceles trapezoid with legs of 10. Find the length of the smaller base.

When I draw a diagram, calling the trapezoid ABCD with A and D at the bottom, I see that the length from where the altitude from B and C hits AC to D is 8 from the pythagorean theorem. But the 6 looks a lot bigger. Also, how to find the smaller base?!

  • Please help with a trapezoid - circle problem -

    AB = CD = 10.
    A = D = 45o.

    h = 10*sin45 = 7.07 = Altitude

    CF = h/sin45 = 7.07/sin45 =10= Diagonal

    BC = EF = CF*cos45 = 10*cos45 = 7.07 =
    Short base.

  • Please help with a trapezoid - circle problem -

    Correction:
    AB = CD = 10.

    h = Diameter = 2*3 = 6=Ht. or altitude.

    Draw altitudes CE and BF

    Draw diagonal CF which bisects BCE and
    BFE. Therefore, CFE = 45o

    tan45 = h/BC = 6/BC
    BC = 6/tan45 = 6. = Shortest base.

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