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.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F446f67cc-d737-4a0c-b4c1-a3db32f7ab90%2F83fa449d-a0bd-4a7b-b790-3ab13aece1c2%2Foua86fp_processed.png&w=3840&q=75)
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F446f67cc-d737-4a0c-b4c1-a3db32f7ab90%2F83fa449d-a0bd-4a7b-b790-3ab13aece1c2%2Fjg3ern_processed.png&w=3840&q=75)
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