BAD LCAD and is the perpendicular bisector of AC In the fig

BAD LCAD and is the perpendicular bisector of AC . In the figure, construct points D and M such that B.

Solution

First of all draw perpendicular bisector of line AC using the steps shown below.

Now draw angle bisector angle A using steps shown below.

Step 3. Draw a line that contains both the vertex and x.Since the intersection points and the vertex all lie on the angle bisector, we know that the line which passes through these points must be the angle bisector.

Now find the intersection point of angle bisector and perpendicular bisector and name it as D.

So you have your desired result.

Step 1. Place the compass at end A and Draw an arc that is centered at the vertex A of the angle. This arc can have a radius of any length. However, it must intersect both sides of the angle i.e AB and AC. We will call these intersection points P and QThis provides a point on each line that is an equal distance from the vertex of the angle.
Step 2. Draw two more arcs. The first arc must be drawn by placing th compass on one of the two points P or Q. It can have any length radius. The second arc must be centered on whichever point (P or Q) you did NOT choose for the first arc. The radius for the second arc MUST be the same as the first arc. Make sure you make the arcs long enough so that these two arcs intersect in at least one point. We will call this intersection point x. Every intersection point between these arcs (there can be at most 2) will lie on the angle bisector.
Step 3. Draw a line that contains both the vertex and x.Since the intersection points and the vertex all lie on the angle bisector, we know that the line which passes through these points must be the angle bisector. Now find the intersection point of angle bisector and perpendicular bisector and name it as D. So you have your desired result.