Question

find ac, if pq is a segment bisector of \overline{ab}.

Explanation:

Step1: Use the property of segment bisector

Since \(PQ\) is the segment bisector of \(\overline{AB}\), then \(AC = CB\). So, \(9x + 18=12x-21\).

Step2: Solve the equation for \(x\)

Subtract \(9x\) from both sides: \(18 = 3x-21\). Add \(21\) to both sides: \(3x=18 + 21=39\). Divide by \(3\): \(x = 13\).

Step3: Calculate \(AC\)

Substitute \(x = 13\) into \(AC=9x + 18\). Then \(AC=9\times13+18=117 + 18=135\).

Answer:

135