jasmyn is standing at the point of tangency to a wishing well, 27 feet from a bench. her friend willard is at the other point of tangency. what is the value of x?
The picture is a circle with a triangle coming out of its side with one side being (2x-7) and the other side being 27 and the side where the circle is connected doesn't have a number.

I assume the picture you're describing is the one I've drawn below. Jasmyn and Willard are at the edge of the wishing well, and the bench is 27 feet from Jasmyn and 2x−7 feet from Willard.

We can draw radius lines from the center of the circle to each point of tangency. These radius lines are perpendicular to the tangent lines. The result is a kite. We can then draw a line from the center of the circle to the bench. This splits the kite into two triangles.

Since both right triangles have the same hypotenuse and the same shorter leg, then their longer legs must also be equal.

2x − 7 = 27

2x = 34

x = 17