Using a ruler and a pair of compasses only,construct triangle abc such that ab=5cm ,triangle bac=45 and abc=30 the locus of l1 of the point equidistant from A and B,the locus l2 of the point equidistant from b and c.Locate p the point of intersection of l1 and l2 using pic as the radius draw a circle
1. Construct line segment AB with length 5cm.
2. Using compass, draw a ray from A at an angle of 45 degrees to AB, marking the point where it intersects AB as C.
3. Using compass again, draw a ray from B at an angle of 30 degrees to AB, marking the point where it intersects with the previous ray as point C.
4. Draw the line segments AC and BC to form triangle ABC.
5. Using compass and ruler, find the midpoint of AB and mark it as point M. Draw a circle centered at M with radius MA or MB, which is the locus l1 of the point equidistant from A and B.
6. Similarly, find the midpoint of BC and mark it as point N. Draw a circle centered at N with radius NB or NC, which is the locus l2 of the point equidistant from B and C.
7. Locate the intersection point of l1 and l2 and mark it as point P.
8. Using compass again, draw a circle centered at P with radius equal to the distance between P and A or B or C to complete the construction.
The final result should be a triangle ABC with a point P that is equidistant from A, B, and C, with circles l1 and l2 representing the locus of points that are equidistant from AB and BC, respectively. The circle centered at P with pic as its radius should also pass through A, B, and C.
To construct triangle ABC with the given conditions:
1. Start by drawing a line segment AB of length 5 cm using a ruler.
2. Place the compass at point A and draw an arc with radius greater than half of AB. Label the point where the arc intersects AB as point D.
3. Without changing the compass width, place the compass at point D and draw an arc to intersect the first arc at point E.
4. Use the ruler to draw a line segment DE.
5. Place the compass at point D and set the width to the length of DE. Draw an arc, making sure it intersects AB. Label the point where this arc intersects AB as point C.
6. Draw the triangle ABC by connecting points A, B, and C with straight lines.
To find the locus of the first point equidistant from A and B (l1):
1. Place the compass at point A and set the width to the distance between A and B (5 cm).
2. Draw an arc that intersects line AB at two points. Label these points as F and G.
3. Draw a line segment FG, which will be l1.
To find the locus of the second point equidistant from B and C (l2):
1. Place the compass at point B and set the width to the distance between B and C.
2. Draw an arc that intersects line BC at two points. Label these points as H and I.
3. Draw a line segment HI, which will be l2.
To locate the point of intersection of l1 and l2 (point P):
1. Locate the point of intersection of lines FG and HI. Label this point as P.
To draw a circle with P as the radius:
1. Place the compass at point P and set the width to the desired radius length.
2. Draw a circle centered at P.
This completes the construction of the triangle ABC, the loci l1 and l2, and the circle.
To construct triangle ABC with the given conditions using a ruler and a pair of compasses only, follow these steps:
Step 1: Draw line segment AB of length 5cm using the ruler.
Step 2: Place the compass at point A and draw an arc with radius 5cm to intersect the line AB at point C.
Step 3: With the same radius, place the compass at point C and draw an arc to intersect line AB at point D.
Step 4: Set the compass width to the distance between points D and A, and draw arcs from both points D and C.
Step 5: Let the intersection of the arcs be point E.
Step 6: Draw line segments AC and BC to complete triangle ABC.
Now, let's construct the loci of l1 and l2:
Step 7: To construct the locus l1, place the compass at point A and B simultaneously. Open the compass to any radius greater than half the distance between A and B.
Step 8: Draw arcs below and above the line AB.
Step 9: Repeat the same steps by placing the compass at points B and C to construct the locus l2.
Finally, we'll locate the point of intersection, P, and draw a circle:
Step 10: Extend lines l1 and l2 to intersect each other at point P.
Step 11: Place the compass at point P and draw a circle with any desired radius, using the pencil end of the compass.
Step 12: Label the point where the circle intersects line AB as point Q.
And there you have it! Triangle ABC is constructed with loci l1 and l2, and point P is located by the intersection of l1 and l2. A circle is drawn with point Q as the radius.