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

Tutors, sign in to answer this question.

Rachelle W. | Professional TutorProfessional Tutor

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**

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## Comments

Oops. 8y = 4 translats to y = 1/2