## 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