Answer:
Step-by-step explanation:
(a) Any pair of points on the circle that are separated by less than the diameter will define a minor arc. (The minor arc is the shortest arc of the circle between the points.) Possible minor arcs in this diagram are ...
VX, VY, XY
The corresponding major arc is usually named by adding the name of a point between the two endpoints that is not on the minor arc. For the minor arcs above, the corresponding major arcs are ...
VYX, VXY, XVY
Given that part (b) tells us the minor arc of interest is 112°, we assume that arc is the one subtended by the chord: XY.
Then, per the discussion above, the corresponding major arc is XVY.
___
(b) The sum of major and minor arcs is the whole circle, 360°. So, the measure of the major arc is ...
360° -112° = 248°
___
(c) A tangent line intersects a circle at exactly one point. It is perpendicular to a radius to that point of intersection. The tangent line in this diagram is UV.
A secant intersects a circle in two places. The portion of the secant between the points of intersection is called a <em>chord</em>. The secant line UX contains the chord XY.
___
(d) A rule of secants (and chords) is that the product of distances from where the secants (or chords) meet to the two intersection points with the circle is the same. For a tangent line, effectively, the two points of intersection are at the same distance. This means ...
UV·UV = UX·UY
UV² = 9·(9+11) = 180
UV = √180 = √(6²·5)
UV = 6√5 ≈ 13.42
_____
The attached figure is drawn to scale with arc XY being 112°.
Given
R is the interior of ∠ TUV.
m∠ RUV=30degrees, m∠ TUV=3x+16, and m∠ TUR=x+10.
Find the value of x and the m ∠TUV.
To proof
As given in the question
m ∠TUV=3x+16, and m ∠TUR=x+10
thus
m∠ RUV = m∠ TUV - m∠ TUR
= 3x + 16 - x -10
= 2x + 6
As given
m ∠RUV=30°
compare both the values
we get
30 = 2x + 6
24 = 2x
12 = x
put this value in the m ∠TUV= 3x+16
m ∠TUV= 12× 3 +16
= 52°
Hence proved
Answer:
Step-by-step explanation:
For this case we need a line parallel to the plane x z and yz. And by definition of parallel we see that the intersection between the xz and yz plane is the z axis. And we can take the following unitary vector to construct the parametric equations:
Or any factor of u but for simplicity let's take the unitary vector.
Then the parametric equations are given by:
Where the point given
And then since we have everything we can replace like this: