Step 1: Construct triangle ABC. Draw a line segment BC of length $10 \text{ cm}$. At point C, construct an angle of $60^\circ$. To do this: Place the compass at C and draw an arc that intersects BC. Without changing the compass radius, place the compass at the intersection point on BC and draw another arc that intersects the first arc. Draw a ray from C through this intersection point. This ray forms a $60^\circ$ angle with BC. At point B, construct an angle of $45^\circ$. To do this: First, construct a $90^\circ$ angle at B. Extend BC to the left. Place the compass at B and draw an arc intersecting the line at two points. From these two points, draw arcs above B that intersect. Draw a ray from B through this intersection point to form a $90^\circ$ angle with BC. Bisect the $90^\circ$ angle. Place the compass at B and draw an arc intersecting the $90^\circ$ ray and BC. From these two intersection points, draw arcs that intersect within the angle. Draw a ray from B through this intersection point. This ray forms a $45^\circ$ angle with BC. The intersection of the $60^\circ$ ray from C and the $45^\circ$ ray from B is point A. Step 2: Construct Locus X, the locus of points equidistant from B and C. This is the perpendicular bisector of the line segment BC. Place the compass at B and open it to a radius greater than half the length of BC. Draw arcs above and below BC. Without changing the compass radius, place the compass at C and draw arcs that intersect the previous arcs. Draw a straight line connecting the two intersection points of the arcs. This line is Locus X. Step 3: Construct Locus Y, the locus of points 1/2 of points from A. We interpret "1/2 of points from A" as the locus of points at a distance of half the length of BC from A. Calculate the radius: $R = \frac{1}{2} \times BC = \frac{1}{2} \times 10 \text{ cm} = 5 \text{ cm}$. Set the compass to a radius of $5 \text{ cm}$. Place the compass point at A. Draw a circle. This circle is Locus Y. Step 4: Find the points of intersection of Locus X and Locus Y. The points where the perpendicular bisector (Locus X) intersects the circle (Locus Y) are the required points of intersection. Mark these points. That's 2 down. 3 left today — send the next one.