Search Results for “intersections”
circle intersections
Can you conjecture a formula for the product of the two distances from a point to a circle?
Locus of intersection of reflected rays
The reflection of parallel rays from symmetric points on a parabola intersect on a circle
Tridecagon Diagonals, Circles and Tangents
You'll want to start out with the heptagon and work your way up. This one's the same as all the others, just with a 13-sided regular polygon. Observe the tangencies to diagonals of circles centered at intersections of diagonals, when the circles are resized (by dragging). This is a smaller version that works well on most monitors (zoom in with two-finger touch). Bigger version here.
Tridecagon Diagonals, Circles and Tangents (BIG)
You'll want to start out with the heptagon and work your way up. This one's the same as all the others, just with a 13-sided regular polygon. Observe the tangencies to diagonals of circles centered at intersections of diagonals, when the circles are resized (by dragging). This is a bigger version that works better on very large monitors in fullscreen mode. Smaller version here.
Circles, Tangents, and Heptagon Diagonals
Two circles are centered at intersection points of diagonals of a regular hepatgon. It turns out that circles centered at intersection points in regular polygons (particularly interestingly with polygons of odd numbers of sides) can be tangent to many other diagonals of that polygon. Try resizing the circles by dragging the green points. How many diagonals can each circle be tangent to? Ready for more? Check out the nonagon version!
Two ways of finding the Fermat Point
This simulation finds the Fermat point as the equilibrium position of the knot in 3 pieces of string, and as the intersection of the perpendiculars to a spring loaded equilateral triangle. Try dragging the corners of the yellow triangle.
A Locus Problem
The locus of the Center of Gravity of the triangle OBA' is shown. (B is the intersection of the line OA with the inner circle, A' is the image of A under reflection in the x-axis) Looks like an ellipse. Is it? If so, what are the foci in terms of the circle radii.
Train Problem
Train AB leaves the station at a constant speed, while train CD approaches the station at a different constant speed. We trace the locus of the intersection of the lines joining the fronts of the trains and their backs. You can drag B to see the trains move, change their lengths and relative speeds.
A geometry theorem
H1,H2 and H3 are feet of altitudes, M1,M2,M3 are midpoints. H is the orthocenter. X2,X3,Y1,Y3,Z1,Z2 are formed by reflecting H1,H2 and H3 in the other altitudes. X,Y,Z are the intersections between the lines joining midpoints to these reflected points. Observe that H appears to be the incenter of XYZ so long as ABC is acute angled. Otherwise it appears to be one of the excenters
