Question

in the figure below, $overline{jm}$ and $overline{jk}$ are tangent to the circle centered at o. the segment $overline{mk}$ passes through the center of the circle. given that $jm = 15.9$ and $mk = 8.4$, find $ml$.

Explanation:

Step1: Recall tangent - secant property

If two - tangents are drawn from an external point to a circle, then the lengths of the two tangents are equal. So, \(JM = JK = 15.9\).

Step2: Use segment subtraction

We know that \(MK=8.4\) and \(MK = JK - ML\). Rearranging the formula for \(ML\), we get \(ML=JK - MK\).

Step3: Substitute values

Substitute \(JK = 15.9\) and \(MK = 8.4\) into the formula \(ML=JK - MK\). Then \(ML=15.9 - 8.4\).

Step4: Calculate the result

\(ML = 7.5\).

Answer:

\(7.5\)