3 years ago

My sister needs help so here I am "helping her" so yeah

Mathematics

2 answers:

Butoxors [25]3 years ago

7 0

1. C
2. D
3. C
Inequalities

pantera1 [17]3 years ago

6 0

1. c
2.d
3.c
hope this helps

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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

elena-14-01-66 [18.8K]

Answer:

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,

$x+5x=360^{\circ}\\ \\6x=360^{\circ}\\ \\x=60^{\circ}.$

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

$\angle BAO=\dfrac{1}{2}(180^{\circ}-60^{\circ})=60^{\circ}.$

Since line CD is tangent to the circle,

$\angle CAO=90^{\circ}.$

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