Question

a student constructs a line tangent to circle o at point p on the circle. she followed the given steps. step 1: draw a line from the center o through p that extends beyond the circle. step 2: with a compass on p, draw an arc on each side of p and label q and r. step 3: with a compass on q, set its width equal to qp and make an arc. step 4: with the compass on r, using the same width as the previous step, make another arc intersecting the previous arc and label the intersection s. step 5: draw a line through p and s. which step contains an error and how can it be fixed? a. step 3: set the width greater than qp. b. step 4: set the width of the compass equal to op. c. step 2: set the compass on o, not p. d. step 5: draw a line through o and s.

Explanation:

Step1: Analyze step - by - step construction

The correct way to construct a tangent to a circle at a point \(P\) on the circle:

1. First, draw a line from the center \(O\) to the point \(P\) (radius).
2. Then, construct a perpendicular to the radius \(OP\) at point \(P\).

In the given steps, step 2 has an error. When constructing a tangent, we need to construct a perpendicular at the point of tangency. The steps seem to be following a wrong approach for constructing a tangent. We should be constructing a perpendicular to the radius at the point of tangency on the circle. The correct way after drawing the radius \(OP\) is to construct a perpendicular to \(OP\) at \(P\), not to set the compass on \(O\) as in step 2.

Answer:

B. Step 2: Set the compass on \(O\), not \(P\)