Question

select the correct answer. a student constructed tangent lines to circle o, passing through point p outside the circle. he followed the given steps. step 1: draw a segment from the center o to p. step 2: construct the perpendicular bisector of segment op. label the mid - point m. step 3: set the compass width to be greater than mo. step 4: from point m, draw an arc across the circle and label the intersections n and q. step 5: draw a line from n to p and another line from q to p. which step contains an error and how can it be fixed?

Explanation:

Step1: Analyze step - by - step construction

The correct steps for constructing a tangent from a point outside a circle to the circle involve first finding the mid - point of the line segment joining the center of the circle and the external point. Then, using this mid - point as the center and half of this line segment as the radius, an arc is drawn which intersects the circle at the point of tangency.

Step2: Identify the error

In step 3, setting the compass width to be greater than $MO$ is incorrect. When constructing a tangent from an external point $P$ to a circle with center $O$, we should set the compass width to be half of the length of $OP$ (after finding the mid - point $M$ of $OP$).

Step3: Determine the fix

Set the compass width to be half of the length of segment $OP$ (after finding the mid - point $M$ of $OP$) instead of setting it to be greater than $MO$.

Answer:

Step 3 contains an error. To fix it, set the compass width to be half of the length of segment $OP$ after finding the mid - point $M$ of $OP$.