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Consider the figure below. Point A is surrounded by 2 pentagons and decagon.Ifpoint B is surrounded similarly, what is n? Why? Ifpoint C is surrounded similarly, wh...

Question

Consider the figure below. Point A is surrounded by 2 pentagons and decagon.Ifpoint B is surrounded similarly, what is n? Why? Ifpoint C is surrounded similarly, what is m? Why? If point D is surrounded similarly, what is p? Why? If parts b, and arc done_ what is the resulting arrangement around point E? What conclusion does this lead to?

Consider the figure below. Point A is surrounded by 2 pentagons and decagon. Ifpoint B is surrounded similarly, what is n? Why? Ifpoint C is surrounded similarly, what is m? Why? If point D is surrounded similarly, what is p? Why? If parts b, and arc done_ what is the resulting arrangement around point E? What conclusion does this lead to?



Answers

Equilateral $\triangle A B C$ is inscribed in a circle. $P$ and $Q$ are midpoints of $\overline{B C}$ and $\widehat{C A},$ respectively. What kind of figure is quadrilateral $A Q P B$ ? Justify your answer.

So we have circle. I mean start, we have Triangle ABC and we know that P is inside this triangle, so it's somewhere inside. It is equal distance from a so we want to know where it's located, so it can't be located on A and B because it is inside the perpendicular by sector of a B. That is true because if it's perpendicular, have a point. Is on the par particular by sector of a line than it. It means that it's equal distance from those two points. It can't be on a C because again it has to be inside and then the perpendicular by sector B. C. So since it needs to be equal distance from A and B, it's not gonna be on the perpendicular by sector of A C. So your answer choice has to be bi

So we have circle. I mean start, we have Triangle ABC and we know that P is inside this triangle, so it's somewhere inside. It is equal distance from a so we want to know where it's located, so it can't be located on A and B because it is inside the perpendicular by sector of a B. That is true because if it's perpendicular, have a point. Is on the par particular by sector of a line than it. It means that it's equal distance from those two points. It can't be on a C because again it has to be inside and then the perpendicular by sector B. C. So since it needs to be equal distance from A and B, it's not gonna be on the perpendicular by sector of A C. So your answer choice has to be bi

All right, so we has our circle. You were told that d e by six Q p. This could make this in this equal. You're converted, right? Took with these air parallel. Want to know if this IHS half of this? So let's create trying going from here to here. Okay, so that's a right ankle. Correct. Right. Well, in this right triangle, this is a This is a radiance. And this is half a radius. Okay? Because this is a whole radio, so that's half radius. So I have the radius squared equals 1/2 radius squares. Plus, Anderson called his ex for frenzies X squared. Okay, so let's simplify this. It's this grisly radius squared equals 1/4 radius squared plus x square. So then, if I subtract fourth radius squared, those size of get three forced radius clear equals X squared unify route. Both those that have discolored of 3/2 radius equals sex. So that right here, square root of 3/2. Or which means that iss where he had freed about it. But outside part, it's a lease to together, so d e u calls twice square root is read about it, but to our, which is square brewed with three car. Okay, well, I maybe this is a radius. And this is the right ISS equals two radius. So Silien, these so square right? Three are is not equal. Teoh. I wouldn't have a to our So that's 33. Art is an equal more so it looks like that would not be correct.

For part A The point of lines on the origin. So its coordinates would be 0:00. 4.8. It lies to be above the X axis. So its coordinates would be zero comma to be four point B. It lies to A to the right of the origin and to be above the X axis. So its coordinates would be to a comma to be okay. and for the coordinates of seat flies to 8 to the right of the original x axes. So it'll be to a comma zero for part B. The coordinates of M, which is the midpoint of A. And O would be zero plus 0/2 comma zero plus you be over to using the midpoint formula which is zero comma to be sorry? Um zero comma B. Um And then The coordinates of Point B which is seven point of points BNC would be To a plus to a over 2:00 to be. But we're too which would be to a comedy. The coordinates of point Q which is the midpoint of seeing, Oh would be to a over 2:00, which is a comma zero. And at that point a point in which is a midpoint of A. And B would be a comma to be using the formula used for um for part C. We need to find a slope of Mq. Yeah. Which would be using the flip formula, it would be B -0-0 -8, which is negative B over a. The slope buff Q P Would be B -0 0 over to a minus A. Which is B over A. The slope of P. N would be two B -B over a minus to B, which is negative B over A. And the slope of um Amen it would be b minus to be over zero minus A. Which is the over eight. So we notice how the slopes of the opposite sides are equal, so the opposite sides are parallel because they have the same slope. So we can conclude that um and PQ is a parallelogram. Um and then for party, the distance between the distance between M and Q yes, square root of 0 -8 squared plus B minus zero squared, which is square root of a squared plus B square. The distance between Q B is again the same. The distance between PN is also the same and the distance between Eman is also scared of a squared plus B squared. So we see that all the sides are equal and it's a parallelogram. So we can conclude that the quadrilateral M n p Q is a robust.


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