Answer:
[tex]AB = \frac{11}{2}[/tex]
Step-by-step explanation:
Given
The above diagram
[tex]AB = 3y + 4[/tex]
[tex]AC = 11y[/tex]
Required
Determine length AB
Tangents drawn from the same point of a circle are equal;
This implies that
[tex]AB = AC[/tex]
Substitute values for AB and AC
[tex]3y + 4 =11y[/tex]
Subtract 3y from both sides
[tex]3y - 3y + 4 = 11y - 3y[/tex]
[tex]4 = 8y[/tex]
Divide both sides by 8
[tex]\frac{4}{8} = \frac{8y}{8}[/tex]
[tex]\frac{4}{8} = y[/tex]
[tex]\frac{1}{2} = y[/tex]
Substitute [tex]\frac{1}{2}[/tex] for y in [tex]AB = 3y + 4[/tex]
[tex]AB = 3 * \frac{1}{2} + 4[/tex]
[tex]AB = \frac{3}{2} + 4[/tex]
[tex]AB = \frac{3 + 8}{2}[/tex]
[tex]AB = \frac{11}{2}[/tex]
