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

Saturday, June 29, 2013

Regular Polygon Inscribed in a Circle

  • With centre O , draw the given circle.
  • Draw a diameter AB and divide it into five equal parts (same number of parts as the number of sides) and number them as shown.
  • With centres A and B and radius AB , draw arcs intersecting each other at M.
  • Draw a line joining points M and A_2 intersecting the circle at I. Then AI is the length of the side of the pentagon.
  • Starting from I , step – off on the circle, divisions IJ , JK , KL equal to AI.
  • Draw segments AI , IJ , JK ,KL and LI thus completing the pentagon.


Thursday, June 27, 2013

Continuous Curves of Circular Arcs

Let A , B , C , D and E are the given points.

  • Draw line segments joining A with B , B with C , C with D and D with E.
  • Draw perpendicular bisectors of AB and BC , intersecting each other at P.
  • With P as centre and radius PA (or PB or PC) , construct an arc. This arc will pass through points A , B and C.
  • Draw a line through P and C.
  • Draw the perpendicular bisector of CD intersecting line through P and C at Q.
  • With Q as centre , and radius QC (or QD) , construct an arc , passing through points C and D.
  • Repeat the process. Please keep in mind that the centre of the arc is at the intersection of the perpendicular bisector and the line joining the previous centre with the last point of the previous arc.
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