Given:
The given circle with center at C. The lines AB and AD are tangents to the circle C.
The length of AB is (3x + 10)
The length of AD is (7x - 6)
We need to determine the value of x.
Value of x:
Since, we know the property of tangent that, "if two tangents from the same exterior point are tangent to a circle, then they are congruent".
We shall determine the value of x using the above property.
Thus, we have;
AB = AD
Substituting the values, we get;
[tex]3x+10=7x-6[/tex]
Subtracting both sides of the equation by 7x, we get;
[tex]-4x+10=-6[/tex]
Subtracting both sides of the equation by 10, we get;
[tex]-4x=-16[/tex]
Dividing both sides of the equation by -4, we get;
[tex]x=4[/tex]
Thus, the value of x is 4.
