\( \overline{J K} \) and \( \overline{J L} \) are tangent to the circle. Find the length of \( \overline{J L} \).

Step 1 ：Let \(O\) be the center of the circle, \(\overline{J K} \) and \( \overline{J L} \) are tangent to the circle at points \(A\) and \(B\), respectively.

Step 2 ：By the tangent and radius theorem, \(\angle OAJ = \angle OBL = 90^\circ\). Hence, \(OJ\) is the geometric mean of \(JA\) and \(JL\).

Step 3 ：Apply the Pythagorean theorem to triangle \(\Delta OAJ\): \(OJ^2 = OA^2 - AJ^2\)

Step 4 ：Apply the Pythagorean theorem to triangle \(\Delta OBL\): \(OJ^2 = OB^2 - BL^2\)

Step 5 ：Set the two equations equal to each other: \(OA^2 - AJ^2 = OB^2 - BL^2\)

Step 6 ：Plug in the given values: \((10)^2 - (8)^2 = (10)^2 - BL^2\)

Step 7 ：Solve the equation for \(BL\): \(BL^2 = 36\)

Step 8 ：Take the square root to find the length of \(\overline{J L} \): \(BL = \sqrt{36}\)

Step 9 ：Answer: \(BL = 6\)