Question

AB and AC are tangent. Find AB

Answer 1

`AB = (11)/(2)`

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

`(4)/(8) = (8y)/(8)`

`(4)/(8) = y`

`(1)/(2) = y`

Substitute
`(1)/(2)` for y in
`AB = 3y + 4`

`AB = 3 * (1)/(2) + 4`

`AB = (3)/(2) + 4`

`AB = (3 + 8)/(2)`

`AB = (11)/(2)`