-1

# ab and ac are tangent to P find ab

ab= 2

ab= 11/2

ab= 1/2

ab=10

in the actual question, AC= 11y

AB= 3y+4

### 2 Answers by Expert Tutors

Rachelle W. | Professional TutorProfessional Tutor
5.0 5.0 (6 lesson ratings) (6)
-1

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

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

Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)
-1

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