pre-calculus

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find the area of the segment formed by a chord 24 cm long in a circle of radius 13 cm.

  • pre-calculus -

    Draw a perpendicular from the center of the circle to the chord.

    So, now we have a central angle a, subtending the chord, such that

    sin(a/2) = 12/13

    Now the area of the minor segment is the area of the sector subtended by the chord, less the area of the triangle.

    The height of the triangle is sqrt(13^2 - 12^2) = 5.

    A = 1/2 r^2 * a - 1/2 * 24 * 5

  • pre-calculus -

    13

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