RELATeD positions
Geometry
 
1. how STRAIGHT LINES AND CIRCLES relate to each other
A straight line is called exterior when the distance d from the centre of the circle to the straight line is longer than the radius of the circle; a tangent if the distance from the straight line to the centre of the circle is equal to the radius and a secant when the distance is shorter.
 

Move the straight line by dragging the red point with the mouse and place it in different positions with respect to the circle.

1.- In your exercise book draw a circle with a radius of 3cm and draw straights lines that are situated 5cm, 3cm and 2cm away from the centre of the circle. Label the lines exterior, tangent and secant.
2. How two circles relate to each other
The relationship between two circles depends on the distance between their central points and the lengths of their radii. If we take d to be the distance between the central points of two circles, they are referred to as exterior if d is greater than the sum of the two radii; exterior tangents if d equals the sum of the two radii; secants if d is less than the sum of the two radii but greater than the difference between them; interior tangents if d is equal to the difference between the two radii; interior if d is less than the difference between the two radii and greater than zero and concentric if d is zero.
2.- Move one of the circles in this window to get an example of each of the pairs of circles explained above. 

 

 

3.- Which examples of pairs of circles have circles with same radius and which do not?

 
       
           
  Miguel García Reyes
 
Spanish Ministry of Education. Year 2001
 
 

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