What is the circle of Apollonius?

What is the circle of Apollonius?

The circles of Apollonius of a triangle are three circles, each of which passes through one vertex of the triangle and maintains a constant ratio of distances to the other two. The isodynamic points and Lemoine line of a triangle can be solved using these circles of Apollonius.

How do you construct a circle tangent to three circles?

Construct the radical center of the three circles, and from that point, draw a line to each of the three poles. In this case, each line intersects its respective circle at two points. The six intersection points are points of tangency for two solution circles, with three tangent points on each solution.

What is the radical axis of two circles?

A radical axis of two circles is the locus of a point that moves in such a way that the tangent lines drawn from it to the two circles are of the same lengths. The radical axis of 2 circles is a line perpendicular to the line joining the centres. Consider two circles S1 and S2 with centres c1 and c2.

Who created the Apollonian Gasket?

Apollonius discovered that there are two other non-intersecting circles, C4 and C5, which have the property that they are tangent to all three of the original circles – these are called Apollonian circles.

How do you construct a radical axis?

The construction is surprisingly simple: Draw any circle C(E,F) that intersects both A(B) and C(D) – one, say, in points G,H, the other in points I,J. Let K be the intersection of GH and IJ. The radical axis of A(B) and C(D) is the line through K perpendicular to the line of centers AC.

How do you construct a tangent to a circle without using the center?

Draw Any Circle. Take Any Point a on It and Construct Tangent at a Without Using the Centre of the Circle. – Geometry

  1. Steps of Construction:
  2. Step 1: Draw a circle with any radius and mark any point A on it.
  3. Step 2: Draw chord AB and an inscribed ∠BCA.

How do you draw a tangent in engineering drawings?

Join A to the centre of the circle O. Bisect line AO so that point B is the mid-point of AO. With centre B, draw a semi-circle to intersect the given circle at point C. Line AC is the required tangent.

Is an Apollonian Gasket a fractal?

In mathematics, an Apollonian gasket or Apollonian net is a fractal generated by starting with a triple of circles, each tangent to the other two, and successively filling in more circles, each tangent to another three.

Is a circle a fractal?

The most iconic examples of fractals have bumps along their boundaries, and if you zoom in on any bump, it will be covered in bumps, etc etc. Both a circle and a line segment have Hausdorff dimension 1, so from this perspective it’s a very boring fractal.