Question

Find the value of x in the following diagram,

3x + 10
Here, B and D are points of tangency.

Answer 1

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;

`3x+10=7x-6`

Subtracting both sides of the equation by 7x, we get;

`-4x+10=-6`

Subtracting both sides of the equation by 10, we get;

`-4x=-16`

Dividing both sides of the equation by -4, we get;

`x=4`

Thus, the value of x is 4.