Question

find the value of x in ⊙q.
5x - 6
2x + 9
x =

Explanation:

Step1: Apply the perpendicular - bisector theorem

Since \(QT\perp LM\) (a line from the center of a circle perpendicular to a chord bisects the chord), we have \(ML = LP\). So, \(5x−6=2x + 9\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
\(5x−2x−6=2x−2x + 9\)
\(3x−6=9\)
Add \(6\) to both sides:
\(3x−6 + 6=9+6\)
\(3x=15\)
Divide both sides by \(3\):
\(x=\frac{15}{3}\)

Answer:

\(5\)