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Search Results for “intersections”

By Nick Halsey
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.

Tags: Tridecagon, diagonals, circles, tangents, intersections, puzzler, intricate, confusing, wow

By Duncan
circle intersections
Can you conjecture a formula for the product of the two distances from a point to a circle?

Tags: circle, tangent

By Phil Todd
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

Tags: orthocenter, incenter

By admin
Circle Pedal
Given a curve and a pole point, the pedal is the locus of the intersections between the tangents to the curve and the perpendiculars through the pole point.  In this case the given curve is a circle, and the pole is the red point.  Try dragging the pole and observe how the clock face changes.  Press the Explain button to see the situation more clearly.

Tags: clock

By Phil Todd
Polar Line
The locus of the intersections of the tangents at the end of chords of an ellipse which pass through a common point is a straight line. A bit of a mouthful, but play with the diagram and it will become clear.

Tags: locus, polar, ellipse, conic

By Phil Todd
Hyperbola Polar Line
The polar line is the locus of the intersections of tangent lines at the ends of chords of teh parabola through a fixed point. Turns out to be conceptually important - not just a curiosity.

Tags: polar, conic, hyperbola

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