Chapter E, Problem 10.6EX

To determine

To choose: The correct option that is useless to construct a tangent to given $\odot O$ form a point P outside the circle.

Answer to Problem 10.6EX

The correct option is (d).

Explanation of Solution

Given information: Consider a circle with center O and a point P outside the circle.

Calculation:

To construct a tangent to circle with center $\odot O$

from point P outside the circle follow the steps given below:

1. Connect points O and P to draw line $\overline{OP}$ .

2. Construct the perpendicular bisector of $\overline{OP}$ to find the midpoint.

3. Consider M as the center and MP as the radius. Now, draw a circle. It can be seen that the circle intersect $\odot O$ at point X .

4. Connect points O and X to draw line $\overline{OX}$ .

  

Figure (1)

From the figure it can be seen that $\overrightarrow{PX}$ is tangent from point P on the circle $\odot O$ .

So, to draw a line parallel to $\overline{OP}$ is useless to draw the tangent.

Therefore, the correct option is (d).