Search Results for “circumcircle”
Circumcircle Construction
Press the Construct button to see how to construct the circumcircle of triangle ABC. You can drag the vertices of the triangle.
Parabola Tangent Circumcircle
3 tangents of a parabola form a triangle. Its circumcircle passes through the parabola's focus.
Simpson Line
Point E lies on the circumcircle of triangle ABC. The projections of E onto the sides of the triangle are colinear. The envelope of such lines forms a deltoid curve. Try dragging E round the circle. Try dragging A B and C. Note that the envelope curve appears to remain equilateral.
Area Under a 4 bar linkage
Drag B and find the configuration with the greatest area. Now press the Show Circle Button. The circle is the circumcircle of A B and D. Does C also lie on it? Now try to find the minimum area.
Regiomontanus Problem
We seek the place on the earth's surface where a vertically suspended bar (or the rings of Saturn) look the biggest. A machine to solve this problem consists of a mass fixed to the earth's surface and a couple of bars attached to the mass and constrained to pass through the ends of the bar. A spring between the bars pushes them apart. The machine reaches equilibrium when the bars are as far apart as possible, hence finding the solution to Regiomontanus' Problem. You can drag the ends of the bar to change the problem. Press Show to see the circumcircle of the ends of the bar and the mass. You should notice something about the position of this circumcircle at equilibrium. Can you explain what you have noticed?
Simpson Line and 9 point Circle
The envelope of the Simpson line is seen to be tangent to the 9 point circle and to touch the concentric circle of 3 times the radius.
Maximum Area Configuration of a Four Bar Linkage
You can set the lengths of the four bars in your linkage. Then drag point B till you think it encloses the maximum area. Click the button to examine the area. Click Solution to observe that the solution occurs where all four vertices lie on the same circle.
Maximum Angle of Reflection
Drag B to find the maximum angle of reflection. The circumcircle of ABC is the locus of all points which subtend the same angle on chord AC. In general G is inside the circumcircle and so angle AGC < angle ABC. The exception is when B=G.
