# ASSIGNMENT 7

Given two circles and a point on one of the circles, construct a circle tangent to the two circles with one point of tangency being the designated point.

Steps to Follow in Constructing Tangent Circles in Geometer

Construct the given two circles.  Make one circle larger than the other, with the smaller circle inside the larger circle.

Construct a point on the larger circle by selecting the larger circle and using the Construct tab on the tool bar. Then select 'Point on Circle'.

Construct a point on the small circle u= sing the same steps as in the previous step.  Then, construct a segment from the center point of the small circle to the point that was just constructed.

Construct a line going through the center of the larger circle and the point that we constructed on the large circle in the second step.

Now we need to construct another circle using the point on the larger circle and the radius of the smaller circle. To do this, first select the point on the larger circle and then select the segment that marks the radius of the smaller circle.  Next, select Construct from the tool bar and then select 'Circle by Center + Radius' from the options.

Construct the intersection point of the circle constructed in the previous step and the line constructed in the step before.  There are two points that intersect the line. Construct the one that is outside of the larger circle.

Construct a segment (blue) from the intersection constructed in the previous step to the center of the smaller circle.

Construct the midpoint of the segment (blue) constructed in the previous step.

Construct a line perpendicular to the segment (blue) that goes through its midpoint.

Construct the point of intersection between the yellow line and the perpendicular line.

Construct a circle using the intersection point constructed in the previous step as the center and passing through the center of the bottom circle.  This circle is constructed using the option 'Circle by Center + Point.

This is our circle that is tangent to the given two circles!