Answer:
[tex]\textsf{B)} \quad \sf \overline{PQ} \cong \overline{PR}[/tex]
Step-by-step explanation:
These are the steps for constructing a tangent line to a circle:
- Draw a circle with center O using a compass.
- Add a point anywhere on the circumference of the circle (point P).
- Draw a straight line from the center O through point P and beyond.
- Place the point of the compass on point P and set it to any width less than the distance OP. Draw two arcs that intersect the line on either side of P. Label the points of intersection of the arcs and the line as Q and R.
- Place the point of the compass on point Q and set it to any width greater than QP. Draw an arc to the left of the line.
- Without changing the width of the compass, place its point on point R and draw an arc intersecting the previously drawn arc. Label the intersection of these two arcs as point S.
- Draw a straight line through points S and P. This is the tangent line to circle O at point P.
In step 4, by placing the point of the compass on point P and drawing two arcs that intersect the line on either side of P without changing the width of the compass, the line segments PQ and PR are equal in length. So, the only true statement from the given answer options is:
[tex]\Large\boxed{\boxed{\sf \overline{PQ} \cong \overline{PR}}}[/tex]
