Question

Segment AB and segment BC are tangent to circle D. Find x if AB = 3x + 8 and BC = 26. Find x.

Answer 1

AB and BC are tangents, so AB = BC.

3x + 8 = 26

3x = 18

x=6

Answer 2

Answer:  The required value of x is 6.

Step-by-step explanation:  We are given that segment AB and BC are tangent to the circle D as shown in he figure.

We are to find the value of x if AB = 3x + 8  and  BC = 26.

We know that

The lengths of two tangents to a circle from any given point are equal.

So, the length of tangent AB and BC are equal.

That is,

$AB=BC\\\\\Rightarrow 3x+8=26\\\\\Rightarrow 3x=26-8\\\\\Rightarrow 3x=18\\\\\Rightarrow x=\dfrac{18}{3}\\\\\Rightarrow x=6.$

Thus, the required value of x is 6.