Question

I need help trying to solve for x IN GEOMETRY

Answer 1

GIVEN:

We are given a circle with a secant and a tangent intersecting outside the circle.

Required;

To calculate the value of x from the information provided.

Step-by-step solution;

"If a secant and tangent are drawn to a circle from the same external point, the products of the length of the secant and its external segment equals the square of the length of the tangent segment."

This is illustrated below;

From the diagram above, the theorem would be applied as follows;

`PC^2=PA* PB`

We now have the following;

`\begin{gathered} (x-1)^2=(x-3)*(x-3+5) \\ \\ x^2-2x+1=(x-3)(x+2) \\ \\ x^2-2x+1=x^2-x-6 \end{gathered}`

Next we collect all like terms;

`\begin{gathered} x^2-2x+1=x^2-x-6 \\ \\ x^2-x^2-2x+x=-6-1 \\ \\ -x=-7 \end{gathered}`

Divide both sides of the equation by -1;

`x=7`

ANSWER:

Option D is the correct answer

`x=7`