• Choice G
    The 2 circles graphed in the standard (x,y) coordinate plane below are centered at the origin, O. In coordinate units, the radius of the smaller circle is 2, and the radius of the larger circle is 4. Points A(−4,0), B, and C(4,0) are on the larger circle. The measure of ∠BOC is 45°.

    45-45-90 triangle ratio

    There are two ratios for 45-45-90 triangles:

    • The ratio of the sides equals 1:1:21:1:\sqrt{2}
    • The ratio of the angles equals 1:1:2

    OD=OB2=42\therefore OD=\frac{OB}{\sqrt{2}}=\frac{4}{\sqrt{2}}

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