Question

AB and AC are tangent. Find AB

Answer 1

Answer:

$AB = \frac{11}{2}$

Step-by-step explanation:

Given

The above diagram

$AB = 3y + 4$

$AC = 11y$

Required

Determine length AB

Tangents drawn from the same point of a circle are equal;

This implies that

$AB = AC$

Substitute values for AB and AC

$3y + 4 =11y$

Subtract 3y from both sides

$3y - 3y + 4 = 11y - 3y$

$4 = 8y$

Divide both sides by 8

$\frac{4}{8} = \frac{8y}{8}$

$\frac{4}{8} = y$

$\frac{1}{2} = y$

Substitute $\frac{1}{2}$ for y in $AB = 3y + 4$

$AB = 3 * \frac{1}{2} + 4$

$AB = \frac{3}{2} + 4$

$AB = \frac{3 + 8}{2}$

$AB = \frac{11}{2}$