Question

1. p is the circumcenter of $\triangle xyz$. use the given information to find $py$. $px = 4x + 3$ $pz = 6x - 11$

Explanation:

Step1: Recall circumcenter property

The circumcenter \( P \) of a triangle is equidistant from all the vertices, so \( PX = PZ = PY \). So we set \( PX = PZ \).
\[ 4x + 3 = 6x - 11 \]

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:
\[ 3 = 2x - 11 \]
Add 11 to both sides:
\[ 14 = 2x \]
Divide by 2:
\[ x = 7 \]

Step3: Find \( PX \) (which equals \( PY \))

Substitute \( x = 7 \) into \( PX = 4x + 3 \):
\[ PX = 4(7) + 3 = 28 + 3 = 31 \]
Since \( PX = PY \), \( PY = 31 \).

Answer:

\( 31 \)