Friday, July 12, 2013

Internal Common Tangents - Unequal Radius

Draw the given circles with centres O and P and radii R1 and R2 respectively such that 
R1 > R2
  1. Draw a line joining the centres O and P.
  2. With centre O and radius equal to (R1 + R2 ), draw a circle.
  3. From P , draw a line PT tangent to this circle.
  4. Draw a line OT cutting the circle at A.
  5. Through P , draw a line PB parallel to OA , on the other side of OP and cutting the circle at B.
  6. Draw a line through A and B. This is the required tangent.
  7. Similarly , draw another internal tangent through C and D.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Friday, July 5, 2013

Common Tangents - Unequal Radius

Draw the given circles with centres O and P and radii R1 and R2 respectively such that 
R1 > R2
  1. Draw a line segment joining centres O and P.
  2. With centre O and radius (R1 - R2 ) , draw a circle.
  3. From P , draw a tangent to the circle drawn in step 2.
  4. Draw a line through O and N to cut the outer circle at B.
  5. Through P , draw a line PD parallel to OB and cutting the circle with radius R2 at D.
  6. Draw a line joining B and D , which is the required tangent.
  7. Similarly , draw another external tangent through E and F.



Monday, July 1, 2013

Common Tangents - Circles with Equal Radius

A. External Tangents
Draw the given circles with centres A and B
  • Draw a line segment joining A and B
  • At A and B construct perpendiculars to AB on its same side to intersect given circles at D and E.
  • Draw a line joining D and E. This line is the required tangent. FG is the other tangent, which can be drawn similarly.
B. Internal Tangents
Draw the given circles with centres P and Q
  • Draw a line segment joining P and Q.
  • Bisect PQ at O. Draw a circle with OP as diameter to cut the circle at M and R.
  • With centre O and radius OM , draw a circle to cut the other circle at S and N.
  • Draw line through M and N. This is the required tangent.
  • Similarly , draw a line through R and S , which is the other required tangent.
This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com