Question

Segment AB and segment BC are tangent to circle D. Find x if AB = 5x + 11 and BC = 3x + 25.

Answer 1

we know that tangents in a circle intersecting at point is always equal in length. we have two tangents AB and BC

by theorm AB=BC

5x+11=3x+25

2x=14

x=7. the length of x is 7

Answer 2

If two tangents drawn on a circle from the same external point then the tangents will be equal.

Here AB and BC are the two tangents of the circle drawn from a point B. So,

AB= BC.

Given AB = 5x + 11 and BC = 3x + 25. Hence, we can set up an equation as following:

5x + 11 = 3x + 25

5x + 11 -3x = 3x + 25 -3x By subtracting 3x from each sides.

2x + 11 = 25

2x + 11 - 11 = 25 - 11 By subtracting 11 from both each sides.

2x = 14

$\frac{2x}{2} =\frac{14}{2}$ Dividing each sides by 2.

So, x= 7