SOLUTION: 4. 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 b

Click here to see ALL problems on Geometric formulas

Question 149170: 4. 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.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
First draw the line segment AB and label it 14 in

Now draw a perpendicular line to the previous one and label it 4 in

We know that the circle is going to go through these points, so go ahead and draw in the circle (note: the circle does not have to be perfect. This is just to give you an idea of what's going on)

Now draw the line segments AC and BC:

Now construct the perpendicular bisectors of AC and BC like this:

Where these two lines intersect will be the center of the circle. Now simply take a ruler and measure the distance from the center to either A, B, or C to get the radius of about 8.12 inches