Question

which statement is true regarding the diagram of circle p? the sum of y and z must be 2x. the sum of y and z must be 1/2x. the difference of z and y must be 2x. the difference of z and y must be 1/2x.

Explanation:

Step1: Recall tangent - secant relationship

If two tangents are drawn from an external point to a circle, the lengths of the two tangents are equal. Let the external point be S. Tangents from S to the circle are of equal length. So, if we consider the lengths of the segments formed by the tangents and secant - like structure in the circle, we know that the sum of the lengths of the two segments (y and z) from the points of tangency on the circle to the intersection points of the non - tangent lines with the circle is equal to the length of the segment (2x) from the external point to the farthest intersection point on the circle. Mathematically, if we use the property of tangents from an external point to a circle, we can prove that \(y + z=2x\).

Answer:

The sum of y and z must be 2x.