Chapter 12.3B, Problem 18A

To determine

(a)

To find:

Conjecture concerning $\overrightarrow{PQ}$ and $\overline{AB}$

To determine

(b)

To prove:

Conjecture concerning $\overrightarrow{PQ}$ and $\overline{AB}$ that $\overrightarrow{PQ}$ bisects line segment $\overline{AB}$ and PQ is also perpendicular to line segment $\overline{AB}$

To determine

(c)

To find:

Conjecture concerning relationship between $\overline{QC}$ and $\angle AQB$ and $\overline{PQ}$ and $\angle APB$

To determine

(d)

To prove:

Conjecture that $\overline{PQ}$ bisects $\angle APB$ and $\overline{QC}$ bisects $\angle AQB$