**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.**

We can think three cases in the
situation above(given
circles have **red** colors) and in each case we can get two kinds(**pink** color and **blue** color)
of tangent circle like the following.(Of couse, there are tangency
cases between each cases)

**Method 1** When the smaller circle is external to
the tangent circle.

(1) Draw the line passing through a center of the bigger circle

(2) Draw a circle with radius of the smaller circle at an intersection getting from (1)

(3) we can get the isosceles triangle above using the property of perpendicular bisector

(4) Our **pink**
circle becomes tangent to two red circles

(1) Draw the line passing through a center of the bigger circle

(2) Draw a circle with radius of the smaller circle at an intersection getting from (1)

(3) we can get the isosceles triangle above using the property of perpendicular bisector

(4) Our **blue**
circle becomes tangent to two red circles

**Method 2** When one circle intersects with another
circle in two different point

We can get the isosceles triangle above as moving of the smalller circle from the method1 using the funtion of GSP.

Our **pink**
and **blue** circle becomes tangent to two red circles

**Method 3** When one circle lies outside of another
circle

We can get the isosceles triangle above as moving of the smalller circle from the method1 using the funtion of GSP.

Our **pink**
and **blue** circle becomes tangent to two red circles

Return to Hyungsook's homepage