Question

What is the value of x in the circle below?204530°60°90°105°150°

Answer 1

The question provides us with a circle and intersecting secants.

The angle formed outside the circle by the secants is 30 degrees while the small arc formed by the secants where they cut the circle initially is 45 degrees.

For better understanding see the figure below:

The secants are AC and AE,

The theorem states that:

"If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment"

The interpretation of this theorem is shown below:

`<\text{BAD}=(1)/(2)(x-<\text{BOD) (By the Intersecting secant theorem}`

Since we know

`\begin{gathered} 30=(1)/(2)(x-45) \\ \text{ Multiply both sides by 2} \\ 30*2=(1)/(2)*2(x-45) \\ 60=x-45 \\ \text{Add 45 to both sides} \\ 60+45=x-45+45 \\ \\ \therefore105=x \\ x=105^0 \end{gathered}`

Thus, the final answer is:

x = 105 degrees (Option 3)