a and b are two points.
shade the region which contains those points which are both closer to a than b and less than 5cm from b.
Unfortunately, as an AI language model, I do not have the ability to create graphical images. However, I can provide a written explanation of the solution.
First, draw a straight line connecting points A and B. This line divides the plane into two regions. Let's call the region containing point A Region 1 and the region containing point B Region 2.
Next, draw a circle with center at point B and radius of 5 cm. This circle represents all points that are exactly 5 cm away from point B.
Now, we need to find the points that are both closer to point A than point B and within the circle of radius 5 cm. These points lie in the shaded region formed by the intersection of Region 1 and the circle of radius 5 cm centered at point B.
To find this shaded region, draw a line segment from point B to the point where line AB intersects the circle. This point (let's call it C) is the closest point on the line AB to point B, but it may not be between points A and B.
Next, draw two additional line segments from point C perpendicular to line AB. Let's call the points where these line segments intersect line AB points D and E.
Finally, draw two additional line segments connecting points A and B to points D and E, respectively. The shaded region is the quadrilateral formed by line segments AD, DE, EB, and the arc of the circle from point D to point E.