Question

check
in ⊙p, ce = fh = 48. find pg.
circle diagram with center p, chords ce and fh, perpendicular segments pd (6x - 3) and pg (3x + 6) to the chords
pg = ____ units

Explanation:

Step1: Use the property of chords

In a circle, if two chords are equal (\(CE = FH\)), then their distances from the center are equal. So, \(6x - 3=3x + 6\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(6x-3x - 3=3x-3x + 6\), which simplifies to \(3x-3 = 6\).
Add \(3\) to both sides: \(3x-3 + 3=6 + 3\), so \(3x=9\).
Divide both sides by \(3\): \(x=\frac{9}{3}=3\).

Step3: Find the length of \(PG\)

Substitute \(x = 3\) into the expression for \(PG\) (\(PG=3x + 6\)).
\(PG=3\times3+6=9 + 6=15\).

Answer:

\(15\)