The length of the common chord of two intersecting circles is 16 meters.
If the radii of the two circles are 10 meters and 17 meters, what is the distance between the centers of the circles, expressed in meters?
Solution to the Problem:
The distance between the centers is 9 meters or 21 meters depending on whether the center of the small circle is in the interior or exterior of the larger circle (see diagrams below).
Use the Pythagorean theorem to solve for two right triangles in each diagram.
Consider the first diagram where the center of the smaller circle is in the exterior of the larger circle:
In the first triangle the hypotenuse is 17 and one leg is 8, so the other leg is 15 meters.
In the second triangle the hypotenuse is 10 and one leg is 8, so the other leg is 6 meters.
So, the distance between the two centers is 15 + 6 = 21 meters.
Mow consider the second diagram where the center of the smaller circle is in the interior of the larger circle:
In the first triangle the hypotenuse is 17 and one leg is 8, so the other leg is 15 meters.
In the second triangle the hypotenuse is 10 and one leg is 8, so the other leg is 6 meters.
But this time, the distance between the two centers is 15 - 6 = 9 meters.
Click here to see Colin Bowey's scale drawing
Correctly solved by:
| 1. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 2. Veena Mg | Bangalore, Karnataka, India |
| 3. Hari Kishan | Meerut, Uttar Pradesh, India |
| 4. Ivy Joseph | Pune, Maharashtra, India |
| 5. Garrett Cannon |
Delta High School, Delta, Colorado |
| 6. Jordan Sollinger |
Woodridge High School, Peninsula, Ohio |
| 7. Kelly Stubblefield | Mobile, Alabama |