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It is relatively straightforward to construct a line t tangent to a circle at a point T on the circumference of the circle: A line a is drawn from O, the center of the circle, through the radial point T; The line t is the perpendicular line to a. Construction of a tangent to a given circle (black) from a given exterior point (P).
Draw circle C that has PQ as diameter. Draw one of the tangents from G to circle C. point A is where the tangent and the circle touch. Draw circle D with center G through A. Circle D cuts line l at the points T1 and T2. One of the required circles is the circle through P, Q and T1. The other circle is the circle through P, Q and T2.
To construct the inverse P ' of a point P outside a circle Ø: Draw the segment from O (center of circle Ø) to P. Let M be the midpoint of OP. (Not shown) Draw the circle c with center M going through P. (Not labeled. It's the blue circle) Let N and N ' be the points where Ø and c intersect. Draw segment NN '. P ' is where OP and NN ' intersect.
Construct the midpoint M of the diameter. Construct the circle with centre M passing through one of the endpoints of the diameter (it will also pass through the other endpoint). Construct a circle through points A, B and C by finding the perpendicular bisectors (red) of the sides of the triangle (blue).
Find the center E of the circle passing through points C, A', and B'. Construct circle E(C), which represents the inversion of the line AB into circle C(r). P and Q are the intersection points of circles C(r) and E(C). [14] If the two circles are (internally) tangential then =, and the line is also tangential.
The center of all rectangular hyperbolas that pass through the vertices of a triangle lies on its nine-point circle. Examples include the well-known rectangular hyperbolas of Keipert, Jeřábek and Feuerbach. This fact is known as the Feuerbach conic theorem. The nine point circle and the 16 tangent circles of the orthocentric system
Draw an arbitrary line (in red) passing through the given circle's center, A, and the desired midpoint B (chosen arbitrarily) on the line m. Notice that the red line, AB, passes through the center of the circle and highlights a diameter, bisected by the circle center. Any parallel may be made from this line according to the previous construction.
the circumcentre, which is the centre of the circle that passes through all three vertices; the centroid or centre of mass, the point on which the triangle would balance if it had uniform density; the incentre, the centre of the circle that is internally tangent to all three sides of the triangle;