Question

given the circle below with secants \overline{jkl} and \overline{nml}, find the length of \overline{jk}. round to the nearest tenth if necessary.

Explanation:

Step1: Apply the secant - secant theorem

If two secants \(LJK\) and \(LMN\) are drawn to a circle from an external point \(L\), then \(LK\times LJ=LM\times LN\). Let \(JK = x\), so \(LJ=LK + JK=11 + x\), \(LM = 12\), and \(LN=LM + MN=12 + 22=34\).
Substitute into the formula: \(11\times(11 + x)=12\times34\).

Step2: Expand and solve the equation

Expand the left - hand side: \(121+11x = 408\).
Subtract \(121\) from both sides: \(11x=408 - 121\).
\(11x=287\).
Divide both sides by \(11\): \(x=\frac{287}{11}\approx26.1\).

Answer:

\(26.1\)