Part 1)
we know that
All circles are similar.
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another. In our attempt to prove all circles are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another
Part 2)
a) ∡BAD=128°-----------> by central angle
b) ∡BCD
The inscribed angle measures half of the arc it comprises.
so
∡BCD=128°/2----> 64°
c) ∡BED
The measure of the external angle is the semi difference of the arcs that it covers.
arc BCD=360°-128°=232°
∡BED=(1/2)*[232-128]-----> 52°
d) What is the relationship between BA and BE?
in the right triangle ABE
∡BEA=∡BED/2-----> 52°/2-----> 26°
tan (∡BEA)=BA/BE------> tan 26°=BA/BE----> BA/BE=0.4877
Part 3)
Find the center and the radius for the circle, given the equation:
x²-14x+y²
+8y=16
Group terms that contain the same variable
(x²-14x)+(y²+8y)=16
Complete the square twice. Remember to balance the equation
by adding the same constants to each side.
(x²-14x+49)+(y²+8y+16)=16+49+16
Rewrite as perfect squares
(x-7)²+(y+4)²=81
(x-7)²+(y+4)²=9²
a) the center is the point (7,-4)
b) the radius is 9
