Introduction to Chords The baobab tree is a species of tree found in Africa and Australia. It is often referred to as th

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Introduction To Chords The Baobab Tree Is A Species Of Tree Found In Africa And Australia It Is Often Referred To As Th 1 (74.05 KiB) Viewed 118 times

Introduction To Chords The Baobab Tree Is A Species Of Tree Found In Africa And Australia It Is Often Referred To As Th 2 (39.91 KiB) Viewed 118 times

Introduction to Chords The baobab tree is a species of tree found in Africa and Australia. It is often referred to as the world's widest tree because it has been known to be up to 45 feet in diameter! While digging at an archeological site, Rafi finds a fragment of a fossilized baobab tree that appears to be wider than any tree on record! However, since he does not have the remains of the entire tree, he cannot simply measure across the tree to Tree determine its diameter. He needs your help to determine the diameter of this fragment ancient tree. Assume that the shape of the tree's cross-section is a circle. a. On it, locate AB, which represents the curvature of the tree fragment. Trace this are on tracing paper. Then, decide with your team how to fold the tracing paper to locate the center of the tree. (Hint: This will take more than one fold.) Be ready to share how you found the center with the class. b. In part (a), you located the center of a circle. Use a ruler to measure the radius of that circle. If I centimeter represents 10 feet of tree, what is the approximate radius and diameter of the tree? Does the tree appear to be larger than 45 feet in diameter? A line segment that connects the endpoints of an arc is called a chord. Thus, AB in the diagram below is an example of a chord. a. One way to locate the center of a circle when given an arc is to fold it so that the two parts of the arc coincide (lie on top of each other). If you fold AB, so that point A lies on point B, what is the relationship between the resulting crease and the chord AB ? Explain how you know. B crease b. The tree fragment in problem 10-48 is an arc between points A and B. However, the missing part of the tree formed another larger are of the tree. With your team, locate the larger arc with endpoints A and B and trace over it in a different color. Propose a way to use the points given to name the larger arc so you can distinguish it from AB c. In problem 10-48, the tree fragment forms the shorter are between two endpoints. The shorter are between points A and B is called the minor are and is written AB The larger arc is called a major arc and is usually written using three points, such as AXB. What do you know about AB if the minor and major ares are the same length? Explain how you know.

In the first problem, folding the are several times resulted in an intersection point that was the center of the circle. But how can you prove that a perpendicular line that bisects an are for chord) will pass through the center of the circle? To consider this, first assume that the perpendicular bisector does not pass through the center a. According to the assumption, if the perpendicular bisector does not pass through the center, then the center, C. will be off the line in the circle, as shown at right. Copy the diagram onto your paper and consider AACD and ABCD. Are these two triangles congruenr? Why or why not? center b. Explain why your result from part (b) contradicts the original assumption. That is, explain why the center must lie on the perpendicular bisector of AB How can you locate the center if all you have is two chords? . For each pair of chords below, determine the center of the circle. Then use a compass to draw the circle. Circle P Circle