Geometry

A secant and a tangent to a circle intersect in a 42 degree angle. The two arcs of the circle intercepted by the secant and tangent have measures in a 7:3 ratio. Find the measure of the third arc.

If someone could help me figure out how to do the equations, then that would be great. Thank you.

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  1. 42° = 1/2 (large-small)
    so, large-small=84°
    but, large = 7/3 * small
    7/3 * small = small+84
    4/3 * small = 84
    small = 63
    large = 147

    So, since the three arcs add up to 360°,

    63+147+x = 360
    x = 150°

    A nice discussion of the topic is found at

    http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php

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  2. given ab is a tangent of point x, ab=70 and xd= 12 what is the measure of db?

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  3. amosc @ unique4418

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