To solve for x, we can use the power of a point property. Simplifying the equation, we get the value of x is 2/3.
The diagram shows a circle divided into two sections by a chord.
The text above the diagram specifies that x, y, and z represent the lengths of the three segments created by the chord.
The problem asks to solve for the value of x.
To solve for x, we can use the power of a point property.
This property states that the product of the lengths of the two segments formed by a secant intersecting a circle is equal to the product of the lengths of the two segments formed by a tangent drawn from the point of intersection to the circle.
In this case, the secant is the chord dividing the circle, and the tangent is the segment labeled 2.
Therefore, we can write the equation:
x * (y + z) = 2^2
We are given that 6 = 3 + z, so we can substitute this value into the equation above:
x * (6) = 2^2
Simplifying the equation, we get:
6x = 4
Finally, dividing both sides by 6, we get the solution for x:
x = 2/3
Therefore, the value of x is 2/3.