A piece of a broken circular gear is brought into a metal shop so that a replacement can be built. A ruler is placed across two points on the rim, and the length of the chord is found to be 14 inches. The distance from the midpoint of this chord to the nearest point on the rim is found to be 4 inches. Find the radius of the original gear. I don't get how to draw this
draw the chord.
Draw the radius through the center of the chord.
Draw a radius to the end of the chord.
If the radius of the gear is r, you can see that
r^2 = (r-4)^2 + 7^2
r = 65/8
To draw the given situation, follow these steps:
Step 1: Draw a horizontal line and label it as the baseline.
Step 2: Choose a point on the baseline and mark it as the center of the gear. Label it as point O.
Step 3: From point O, draw a straight line upwards. This line represents the imaginary axle of the gear.
Step 4: Decide on the radius of the gear and mark a point on the imaginary axle accordingly. Label it as point A.
Step 5: From point A, draw a perpendicular line ending at the baseline. This line represents the exact center of the broken chord.
Step 6: On both sides of point A, mark two separate points on the baseline. Label them as points B and C.
Step 7: Using the ruler, draw the chord BC, connecting points B and C. This chord represents the broken piece of the circular gear.
Step 8: Find the midpoint of the chord BC and mark it as point D.
Step 9: From point D, draw a perpendicular line to the chord BC. This line represents the shortest distance from the midpoint of the chord to the nearest point on the rim.
Step 10: Measure the length of the chord BC. Since it has been given as 14 inches, mark the length on the chord itself.
Step 11: It is also given in the problem that the distance from the midpoint of the chord to the nearest point on the rim is 4 inches. Measure and mark this distance on the line you drew in Step 9.
Step 12: Mark the intersection of lines A and BC as point E.
Step 13: Finally, measure the distance from point A to point E. This length will give you the radius of the original gear.
By following these steps, you will have a clear visualization of the given problem and be able to further solve it.
To draw the situation described, you can follow these steps:
1. Take a piece of paper and a pencil.
2. Draw a straight line, which will represent the ruler. Label the two endpoints of the line as A and B.
3. At the midpoint of line segment AB, draw a perpendicular line. Label the point where the perpendicular line intersects AB as C.
4. Place your compass at point C and set the radius to 4 inches.
5. Draw an arc above line AB, intersecting it at points D and E. Label these points accordingly.
6. Measure and mark a point on AB, 7 inches away from point C. Label this point as F.
7. Connect points F and D with a straight line.
8. Finally, draw a circle with center C and radius CF. This circle represents the original gear.
Now you should have a visual representation of the broken circular gear and the given measurements.