Suppose $LK$ is tangent to circle $J$ at point $K$. If the distance from the center $J$ to point $L$ is $10$ units and the distance from $L$ to $K$ is $6$ units, what is the length of the radius of the circle?

• A. $\sqrt{100-6^2}$ units
• B. $10$ units
• C. $6$ units
• D. $\sqrt{36+{10}^2}$ units

Answer: (A)

Verified step by step guidance

1. Identify the given elements: line segment LK is tangent to circle J at point K, the distance from center J to point L is 10 units, and the distance from L to K is 6 units.
2. Recall the property that a radius drawn to a tangent point is perpendicular to the tangent line. Therefore, segment JK (the radius) is perpendicular to LK at point K.
3. Recognize that triangle JLK is a right triangle with right angle at K, where JK is the radius (unknown), LK is 6 units, and JL is 10 units.
4. Apply the Pythagorean theorem to triangle JLK: \(JL^2 = JK^2 + LK^2\), which translates to \$10^2 = r^2 + 6^2\(, where \)r$ is the radius JK.
5. Rearrange the equation to solve for the radius: \(r^2 = 10^2 - 6^2\), then express the radius as \(r = \sqrt{10^2 - 6^2}\).