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Inscribed and Circumscribed Quadrilaterals
 


The model makes it possible to choose various quadrilaterals and circles, and also to observe their relative position. You can observe if a circle can be inscribed into a quadrilateral (or be circumscribed about it), or it cannot.

At first, you have to choose a quadrilateral into which you want to inscribe (or about which you want to circumscribe) a circle. For this to happen, on the "Change" button panel choose "Quadrilat.", and, by using the Mouse, specify the arrangement of the quadrilateral vertices on the model work area.

Here, in "Important relations" of the pop-up window you can observe the relations between the sides and the angles of a quadrilateral, which states the capability of circle inscribing or circumscribing.

You can now try to inscribe or to circumscribe a circle. For this choose "Circles" on the "Change" panel, and, by using the Mouse, "Angles" panel and "Tools" panel, choosing a radius, try to inscribe the circle into the quadrilateral or to circumscribe the first about the second. If the circle is inscrubed into the quadrilateral, it will change the colour from red to green. If you circumscribe the circle about the chosen quadrilateral, it will be white.

The following order of circle inscribing is recommended. Select the lower button on the "Tools" panel and one of angles on the "Angles" panel. After that the arms of an angle become tangents to a circle. By changing the circle radius, obtain the situation so that the circle is inscrubed into the quadrilateral.

The following order of circle circumscribing is recommended. Select the upper button on the "Tools" panel and one of angles on the "Angles" panel. After that a chosen angle and two adjacent vertices will always lie on a circumference, and changing the location of the centre by the Mouse, obtain the situation when the quadrilateral is inscribed.

By changing parameters of a quadrilateral and a circle, you can verify that only if the defined relations between the angles and the sides of a quadrilateral are satisfied, the quadrilateral can be inscribed or circumscribed. The model illustrates the conditions whose satisfaction makes it possible to inscribe a circle into a quadrilateral or to circumscribe the first about the second.

A quadrilateral can be specified by a figure which provides its changing by the Mouse. In so doing, the numerical values of all sides and angles of a quadrilateral, and also the sums of its opposite angles and sides, are displayed.

To show the diagonals of a rectangle tick off the corresponding window.

If you think it is possible to inscribe a circle into the rectangle (or to circumscribe that about it), choose the respective option. The model will make constructing or give the message of the failure to do so for that quadrilateral.

Notice that in order for a circle should be inscribed into or circumscribed about any quadrilateral, it is necessary to satisfy the defined relations between the values of its angles or between the lengths of its sides.

You need to install ActiveX plug-in to be able to view this model.
You can download it here.


 
© OpenTeach Software, 2007