Question

select the correct answer from each drop - down menu.
point a lies outside of a circle with center o. the given steps describe the process to start constructing a line tangent to the circle and passing through point a using a compass and straightedge.
step 1: draw segment (overline{oa}).
step 2: find the midpoint, m, of (overline{oa}) by constructing the perpendicular bisector of (overline{oa}).
complete the missing information for the construction.
step 3: draw a circle centered at m going through a and o
step 4: let the points b and c represent the points where the two circles meet.
step 5: draw the segments ab and to create two tangent lines to the circle.
options for the last drop - down: ca, oa, ab

Explanation:

1. For Step 3: When constructing tangents from an external point A to circle O, the circle centered at midpoint M of $\overline{OA}$ must pass through O and A to ensure it intersects the original circle at the tangent points.
2. For Step 5: The intersection points of the two circles are B and C. Drawing segments $\overline{AB}$ and $\overline{AC}$ creates the two tangent lines from A to the original circle, as these lines will touch the circle only at B and C respectively.

Answer:

Step 3: M going through A and O
Step 5: AB and AC