1. The circular track is tangent to each side of Quadrilateral ABCD, and all of the angles in Quadrilateral ABCD are right angles. Points W, X, Y, and Z are the points of tangency. Find each of the following. D' mzw a. MWXZ b.

Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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ChapterP: Preliminary Concepts
SectionP.CT: Test
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The renowned architect and graduate of the MIU School of Design, Drew Atower, designed a hotel, all of
whose floors spin on a circular track. As it spins, each floor pauses every 45°. (Otherwise, getting on and off
the elevator would be tricky.) The figure below shows an overhead view of one of the square floors and its
circular track. Points A, B, C, and D are located at each of the four corners of the building. 40 bisects arc ZW.
z, 0, and X are collinear. A, O, and C are collinear.
1. The circular track is tangent to each side of Quadrilateral ABCD, and all of the angles in Quadrilateral ABCD
are right angles. Points W, X, Y, and Z are the points of tangency. Find each of the following.
B
а.
MWXZ
b.
2. Draw AX and and label the point of intersection with the circle as point M. If mžw = 53°, find MLAXB.
3. Draw AC and radius ox. Find each of the following. MLAOX
а.
MLOXA
b. ZCAX intercepts two arcs. Find their measures.
Transcribed Image Text:The renowned architect and graduate of the MIU School of Design, Drew Atower, designed a hotel, all of whose floors spin on a circular track. As it spins, each floor pauses every 45°. (Otherwise, getting on and off the elevator would be tricky.) The figure below shows an overhead view of one of the square floors and its circular track. Points A, B, C, and D are located at each of the four corners of the building. 40 bisects arc ZW. z, 0, and X are collinear. A, O, and C are collinear. 1. The circular track is tangent to each side of Quadrilateral ABCD, and all of the angles in Quadrilateral ABCD are right angles. Points W, X, Y, and Z are the points of tangency. Find each of the following. B а. MWXZ b. 2. Draw AX and and label the point of intersection with the circle as point M. If mžw = 53°, find MLAXB. 3. Draw AC and radius ox. Find each of the following. MLAOX а. MLOXA b. ZCAX intercepts two arcs. Find their measures.
When the building rotates 45°, the corner that was located at point A is now located at point E. Points P, Q, R
and S are the points of tangency.
4. Draw PS and RZ. Find the measure of the angles formed by PS and Rz.
H
R
G
5. A circular stained glass and wrought iron window is to be installed above the front entrance. One of the
stained glass window designs being considered has a radius of 90 cm and several wrought iron chords each
60 cm long. How far are the chords from the center of the circle? Draw a diagram and show your work.
In the main lobby of the hotel, there is a circular hospitality area that also rotates. The radius of the hospitality
area is 3 m. The distance from the front door, at point A, to the far side of the hospitality area, at point C, is 20
m. At a certain moment the dessert bar is located at point B and the tourist information desk is located at point
E.
B,
E
6. Assuming AB and AE are tangent to the circle, find CD and AD. Explain how you arrived at your answers.
Transcribed Image Text:When the building rotates 45°, the corner that was located at point A is now located at point E. Points P, Q, R and S are the points of tangency. 4. Draw PS and RZ. Find the measure of the angles formed by PS and Rz. H R G 5. A circular stained glass and wrought iron window is to be installed above the front entrance. One of the stained glass window designs being considered has a radius of 90 cm and several wrought iron chords each 60 cm long. How far are the chords from the center of the circle? Draw a diagram and show your work. In the main lobby of the hotel, there is a circular hospitality area that also rotates. The radius of the hospitality area is 3 m. The distance from the front door, at point A, to the far side of the hospitality area, at point C, is 20 m. At a certain moment the dessert bar is located at point B and the tourist information desk is located at point E. B, E 6. Assuming AB and AE are tangent to the circle, find CD and AD. Explain how you arrived at your answers.
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