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Line of centres through the point of contact of two circles

The diagram shows two circles with centres A and B. Move the first slider to the right. Move the second slider to draw the line of centres between the two circles. What do you observe?

  1. Consider the common tangent to both circles drawn at the point of contact, C. What is the size of the angle between the common tangent and the radii of both circles?
  2. What would be the size of each pair of adjacent angles formed by the tangent at the point of contact? What does this tell us about the centres of the circles and their point of contact?