Folks, these are the exercises from class. Please make sure to do them if you wish to understand how the theorems pertaining to circles are used. Remember, you will be quizzed on this next week (and it will not be open book).
Page 365-366; #3, 8, 9, 10 and 12
Page 368-369; #4, 9, 13 and 23
Page 371; #8 and 9.
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6 comments:
Does anyone have any suggestions for numbers 9 and 23 on page 368?
For #13 is y=2x? Or have I misinterpreted proposition XX?
I'm in a cafe doing work for tomorrow's class and I don't have my book, but I would like to help you out. So, if you type in the question I can try and help you that way.
9) In the inscribed pentagon ABCDE, AB=AE, angle ABC=114, angle BCD=130 and angle CDE=108. Find the other anlges of the pentagon. (Draw EB.)
23) ABC is an equilateral triangle inscribed in a circle. P and Q are the midpoints of the arcs BC and CA. Prove that AQPB is a rectangle.
Thank you.
My first hint for number 9 is that if you consider quadrilateral BEDC, then you notice that it is inscribed in the same circle that the pentagon is inscribed in. We know that opposite angles of quadrilaterals are supplementary and so you can find CBE as a result. Then by subtraction you can find ABE. Continue from here on and I think the rest should be easy.
For #23, remember that the points P and Q are midpoints of the ARCS BC and CA, not the line segments. Then if you look at any one of those midpoints, then the line joining the midpoint to the center of the circle is also the angle bisector of the central angle formed by the arc, such as arc BC. This also means that it bisects the chord BC. If this is so then the line joining the center and say, P, is collinear with the altitude from A of ABC. Thus AP is a diameter. Now it is very easy to finish the necessary arguments from here on.
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