SOLUTION: What is the measure of minor arc AB? http://imgur.com/q3KpkZn Thank you! :)

Question 997043: What is the measure of minor arc AB?
http://imgur.com/q3KpkZn
Thank you! :)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
check out the bottom of this reference (tangent and secant).
http://www.regentsprep.org/regents/math/geometry/GP15/CircleAngles.htm

your angle is 20 degrees.

let x be the measure of arc AB.

let b be the measure of arc BC.

from the reference, the formula to find the angle is:

20 = 1/2 * (b - a)

now, since arc AC measures 192 degrees, then we know that arc AB + arc BC must be the difference between that and 360 degrees.

we get a + b = 360 - 192 = 168

because a + b = 168, we can solve for b to get b = 168 - a.

we can replace b in the equation of 20 = 1/2 * (b - a) to get:

20 = 1/2 * (168 - a - a)

combine like terms to get 20 = 1/2 * (168 - 2a)

multiply both sides of this equation by 2 to get 40 = 168 - 2a

subtract 40 from both sides of this equation and add 2a to both sides of this equation to get:

2a = 168 - 40 = 128

divide both sides of this equation by 2 to get:

a = 128/2 = 64

since b = 168 - a, we get b = 168 - 64 = 104.

we now have a = 64 and b = 104

this means that the measure of arc AB is equal to 64 degrees and the measure of arc BC is equal to 104 degrees.

your solution is that the measure of arc AB is 64 degrees.

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