From the length of two tangents 2x + 16 and 4x - 2. The value of x is 9.
The length of one tangent is 2x + 16.
The length of the other tangent is 4x - 2.
Theorem on the length of a tangent
The length of two tangents drawn from an external point to a circle is equal. Let's suppose AP and AQ are two tangents from point A to a circle then AP = AQ.
Consider the length of one tangent to be AP and the other tangent to be AQ from a points A to a circle.
So, from the above theorem, we get
AP = AQ
[tex]\rm 4x-2=2x+16\\\rm 4x-2x=16+2\\\rm 2x=18\\\rm x=9[/tex]
Therefore, from the length of two tangents 2x + 16 and 4x - 2. The value of x is 9.
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