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Math Help - Circle question

  1. #1
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    Circle question

    A point P is 8cm from the centre of a circle of radius length 5cm. Find the length of the major arc between the points of contact of the tangents drawn from P to the circle.

    Thanks in advance.
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by deltaxray View Post
    A point P is 8cm from the centre of a circle of radius length 5cm. Find the length of the major arc between the points of contact of the tangents drawn from P to the circle.

    Thanks in advance.
    this is the graph
    Circle question-31.jpg

    the arc length equal the radius multiply with the arc angle in radian
    so we need to find the angle between the side 8 and the side 5, there is a theorem that said the the line joined from the center to any tangent point is orthogonal to the tangent line from that point

    so the angle equal \cos A = \frac{5}{8}

    A = \cos ^{-1} \frac{5}{8}
    A is the angle between the sides 8,5

    finally
    arc \;  \; length = A (5)
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