Search Results for “tangent”
Relation of tangent slope to derivative
See the relationship of tangent lines in derivatives any graph!
Tangent Triangle
We show the areas of the triangle formed by joining 3 points on a parabola, and that formed by the tangents to the parabola at those points.
Parabola Tangent Circumcircle
3 tangents of a parabola form a triangle. Its circumcircle passes through the parabola's focus.
Archimedes Twins
The large circle is tangent to each of the purple circles, which are tangent to each other. The radius of the large circle is the sum of the radii of the purple circles. The Yellow circles are each tangent to one of the purple circles, to the large circle and to the common tangent of the two purple circles. The yellow circles are called the Archimedes Twins, and have the same radius. Can you work out what this radius is in terms of the radii of the purple circles?
An Arbelos Theorem
The large circle in the diagram has radius 1. Circles centered at A and B are tangent and each tangent to the large circle. (The shape in between the circles is called an arbelos after the Greek for a cobbler's knife, which it apparently resembles.) BC is tangent to circle A and AD tangent to circle B. EF and GH are perpendicular to AB. Can you show that they are equal? Can you find an expression for their length in terms of the radius of circle A? Are they the same size as Archimedes "twins"
A lemma of Archimedes
BF is perpendicular to diameter CD. E is the intersection point of tangents at B and D. Observe that BG = FG. Can you prove it? This is from the Liber Assumptorum (Book of Lemmas) translated from Arabic but attributed to Archimedes.
Euclids Elements - Book 3 - Proposition 14
Creating a tangent on a circle given point A that is outside the circle.
