Question

Segment AB and segment BC are tangent to circle D. Find x if segment AB = -x + 6 and segment BC = 3x + 1. Find x.

Answer 1

Since, tangent lines AB and BC originates from point B

so, they must be equal

$AB=BC$

we are given

$AB=-x+6$

$BC=3x+1$

so, we can set them equal

$-x+6=3x+1$

now, we can solve for x

$6-1=3x+x$

$4x=5$

$x=\frac{5}{4}$...........Answer