An interactive applet and associated web page that demonstrate the 'Intersecting Secants Theorem'. The applet shows a circle and two secant lines intersecting at a point outside the circle. The secant points and the external point are draggable. As you drag them the secant lines are redrawn and a realtime computation on the applet shows that the product of their segments are always the same. By dragging two secant points together, the Tangent-Secant Theorem is also demonstrated. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Working as a team, students discover that the value of pi (3.1415926...) is a constant and applies to all different sized circles. The team builds a basic robot and programs it to travel in a circular motion. A marker attached to the robot chassis draws a circle on the ground as the robot travels the programmed circular path. Students measure the circle's circumference and diameter and calculate pi by dividing the circumference by the diameter. They discover the pi and circumference relationship; the circumference of a circle divided by the diameter is the value of pi.

An interactive applet and associated web page that demonstrate the radius of a circle. The applet shows a circle with a radius line. The radius endpoints are draggable and the figure changes to ensure the line is always a radius of the circle. Demonstrates the radius is always a constant length for a given circle. See also the entries for circumference and diameter. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate a secant to a circle. (not trig). The applet shows a circle and a secant line. The points where the secant cross the circle are both draggable. As you drag each, the secant line moves. If you carefully make the two points coincide, it shows a message that this is now a tangent line. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

An interactive applet and associated web page that demonstrate a segment of a circle - a part of a circle cut off by a chord. The applet shows a circle and a segment of that circle, the ends of which can be dragged to resize the segment. You can create the situation where the chord is a diameter and so no segments are created. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts — basic geometry and trigonometry — that have been used for thousands of years.

An interactive applet and associated web page that demonstrate a tangent to a circle. (not trig). The applet shows a circle and a tangent line. The center point and the tangent contact point are both draggable. As you drag each, the figure changes to ensure that the line is always tangential to the circle. The line from the center to the tangent point is shown and the angle is shown to be always 90 degrees no matter what you do. The perpendicular and its angle can be turned off for class discussion. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A web page and interactive applet illustrating Thales Theorem (the diameter of a circle always subtends a right angle to any point on the circumference). The applet shows a circle where the user can rotate the diameter and a move a point on the circumference. The applet continuously shows the resulting right triangle, demonstrating that the theorem holds no matter how the points are moved around. Text on the page defines the theorem and relates it to other geometric entities. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

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