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.

x = 17

Step-by-step explanation:

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

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough