POINT • POINT • CIRCLE
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Both Points Outside A Circle
Number of solutions: 2
GeoGebra construction
Steps
- Construct a circle for circular inversion. Choose the point A as its centre and the distance between the assigned points (the line segment AB) as its radius.
- Invert the assigned circle into the newly constructed one with the help of circular inversion.
- After constructing the new circle with c. inversion, construct its tangents which pass through the point B.
- Construct two circles with the circular inversion of tangents of the circle constructed in the first step. The two circles, k1 and k2, are the solution.
GeoGebra construction
Steps
- We have a circle k with center S and points A, B
- Draw a line f passing through points A and B and the perpendicular bisector of segment AB, g
- Draw a circle c with its center on g having an arbitrary radius
- Mark the intersections of c and k as E and F, and label the line EF as h
- Mark the intersection of f and h as G
- From G, draw tangents to k, which we label as i and j
- From the intersections of i and j with k, labeled as H and I, respectively, draw lines HS, labeled as l, and IS, labeled as m
- Mark the intersection of g with m as J and the intersection of g with l as K
- Construct the finalised solution by creating k1, with center at J passing through A, and k2, with center at K passing through A