Circles and Inscribed Right Triangles
This page will allow to explore the relationships between circles and inscribed right triangles. Each page on the left matches a question on your worksheet. Enter the answer on your worksheet, then click the mouse on 'Next' to move to the next question. If you do not understand a word that is underlined, click on the word for an explanation.
If your teacher has given you a worksheet, make sure you fill it out as you go along. Look for the (w) symbol. Whenever this symbol appears on the screen, fill in the answer on the worksheet.
Start by manipulating the figure on the left. First, click on point O and drag the point around. Notice that the center of the circle moves with the mouse. What point does not move when you move point O? (w)
Now, move point A with the mouse. What point does not move now? (w)
Points O and A are independent. This means that they can move without having to move the other one. Now click and drag point B. Notice that you can not move point B by itself. This is because point B is drawn so that it is on the opposite side of the circle from A. Point B is dependent on points O and A.
Now click on point C and drag it. On what part of the figure does point C always stay?
The Circle and Its Diameter
Look at the circle. What point is at the center of the circle? (w)
Notice that points A and B are on the circle. Line segment AB passes through what point other than A and B? (w)
The line segment AB is the diameter of the circle. How would you define the diameter of a circle. Write your definition on the worksheet.(w)
The word diameter comes from the greek words di^a and metrÍtos. 'Di^a' means through the midst of and metrÍtos means measured off. Source: Translatum Website. Together they mean measure through the middle of.
The definition of diameter from Math.com Glossary is: The line segment joining two points on a circle and passing through the center of the circle.
How do these compare with your definition of a diameter?
Right Angle in Triangle ABC
To the left of the circle find the text starting 'mAngle BCA ='. What is the measure of angle BCA? Write this on your worksheet.(w)
Click on point C and drag point C around the circle. How does the measure of angle BCA change? Write the answer on your worksheet.(w)