A, because anything with a dilation will not be congruent as the original PQR :))
Answer:
.
(Expand to obtain an equivalent expression for the sphere:
)
Step-by-step explanation:
Apply the Pythagorean Theorem to find the distance between these two endpoints:
.
Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:
.
In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between
and
would be:
.
In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:
.
The equation for a sphere of radius
and center
would be:
.
In this case, the equation would be:
.
Simplify to obtain:
.
Expand the squares and simplify to obtain:
.
Answer:
°
Step-by-step explanation:
"Theorem 9-13: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs."
Basically no matter what other circle, secant or tangent you get, you just use the formula
If you need the outer angle, just put the other angles in and solve
If you need the far or near point angle, re-arrange the formula to get that value.
The symbol that will make that statement true is <