Chord ab subtends two arcs with measures in the ratio of 1: 5. line l is tangent to a circle at point a. find the measure of the angle between the tangent and secant ab .

30°

Step-by-step explanation:

If chord AB subtends two arcs with measures in the ratio of 1:5, then the measure of minor arc is x and the measure of major arc is 5x. Thus,

Thus, the measure of the angle AOB  is 60°. Consider isosceles triangle AOB (because AO=BO=radius of the circle). The angles adjacent to the base AB are congruent, thus

Since line CD is tangent to the circle,

Hence,

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