possible answers:
ab= 2
ab= 11/2
ab= 1/2
ab=10
in the actual question, AC= 11y
AB= 3y+4
possible answers:
ab= 2
ab= 11/2
ab= 1/2
ab=10
in the actual question, AC= 11y
AB= 3y+4
Two tangents to a circle from the same point outside the circle will always be equal. We set the two expressions equal to each other and solve for y.
11y = 3y + 4
8y = 4
y = 1/2
Once we've found that y = 1/2, we substitute that value back into the original expression for AB and solve.
AB = 3y + 4
AB = 3(1/2) + 4
AB = (3/2) + 4
AB = 11/2
If the two segments are tangent to the same point, then they are congruent (i.e., ab ~ ac).
You are given the following:
ac = 11y and ab = 3y + 4
Since we've already determined that the two segments (ab and ac) and congruent, we can set the expressions that define their lengths equal to one another:
11y = 3y + 4
Now we solve for the unknown variable (y) by first subtracting 3y from both sides of the equation then dividing both sides by the coefficient of y:
11y - 3y = 3y - 3y + 4
8y = 4
8y/8 = 4/8
y = 1/2
To find ab, we plug in the solution for y into the expression defining ab:
ab = 3y + 4
ab = 3(1/2) + 4
= 3/2 + 4
Since one of the terms is a fraction, we need to find a common denominator among the 2 terms so that we can add them. To do so, multiply 4 by 2/2 to get 8/2.
ab = 3/2 + 4(2/2)
= 3/2 + 8/2
= (3+8)/2
ab = 11/2
Comments
Oops. 8y = 4 translats to y = 1/2