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Line of centres of two circles

In the diagram, two circles with centres A and B are shown. Move the slider to change the radii of the two circles. What observations can you make regarding the relationship between the line of centres of the circles and their common chord?

  1. What test could you use to prove that triangles ACB and ADB are congruent?
  2. What does the result from question (1) tell us about <CAB and <DAB?
  3. Using the result from (2), what test could we use to prove that triangles CAF and DAF are congruent?
  4. How can we use the result from (3) to prove that the line of centres bisects the common chord at right angles?