Hi. I need to determine the side lengths of all the chords of a cyclic quadrilateral but it seems to be an abnormal shape? It's given that one diagonal is 50, another 57 and one side is also 50.
Theres also an angle that's 60° but this is create by one of the diagonals and the box, I'm assuming the full angle is 90° but not sure how to prove pls help.
Given cyclic quadrilateral ABCD, how could I prove that <CDB = <CAB? Is this even possible?
If context helps, I've been trying to prove the existence of the Simson line by myself, and knowing this would help me rule out (or prove) some of my hypotheses.
Anything helps, and thanks in advance!
I've got a cyclic quadrilateral but I can find I way to determine the individual side lengths for the shape (seems abnormal) given is the length of both diagonals (50,57), one side (50) and one angle formed from a triangle and outer box (60°) please help.
I suspect that each corner is 90° but I'm not sure how to prove this or how it would help?
Also what is being asked for when they say the relationship between product of diagonals and sides?
http://imgur.com/gallery/BH22vlM
I need the proof for the following formula, as there is a mistake in my book about it (at least I think so...):
In a cyclic quadrilateral ABCD, prove the following,
cos(B) = (a^2 + b^2 -c^2-d^2)/2(ab+cd)
where a, b, c and d are the opposite sides to the angles in the quadrilateral...
Also for anybody who is interested in the error, there is a line in the proof given the book that goes like this...
After you apply Cosine rule in triangle ABC and ACD, you will get the following relation:
AC^2 = a^2 + b^2 - 2ab(cos(B)) = c^2 + d^2 - 2cd(cos(B)) [cos(180-B) = cosB in a cyclic quadrilateral]
a^2 + b^2 - 2ab(cos(B)) = c^2 + d^2 - 2cd(cos(B))
(after these lines, they then give this...)
2(ab+cd)cosB = a^2 + b^2 - c^2 - d^2
(But that doesn't make any sense, how did both the negative Cosine terms become positive? either one should be positive and the other negative..., right?)
Can someone explain what is going on?
https://imgur.com/a/F5cfCjh
This is two pictures of how much I managed to do with the original question as well.
Let ABCD be a quadrilateral, with diagonals AC and BD intersecting at P. Let AD and BC intersect at Q. Prove that the midpoints of QP, AB, and CD are collinear. (degenerate case just when AD and BC are parallel)
Edit: Sorry, mixed up two problems I had involving quadrilaterals :).
Let ABCD be cyclic, with diagonals AC and BD intersecting at P. Let the feet of perpendiculars from P to AD and P to BC be J and K, respectively. Let the midpoints of AB and CD be M and N, respectively. Prove that MN is the perpendicular bisector of JK.
L.D.C.T = \sqrt {d^2 - (R-r^2)}
L.T.C.T = \sqrt {d^2 - (R+r^2)}
What is the full form of LDCT and LTCT in cyclic quadrilateral?
Or are there restrictions on the side lengths of cyclic quadrilaterals (along the lines of how a right triangle side lengths must obey the Pythagorean theorem)? Thanks!
http://i.imgur.com/kXS53.png
Not really sure where to start with this at all. I've written things down like equal angles and added lines to show what should be happening. But nothing seems to lead anywhere. Any ideas? Hate asking about geometry proofs, but sometimes I just can't come up with anything for them.
Edit: How I feel after making this post
So in the latest episode of Wonder Egg Priority one of the trauma's posed a question to Neiru and one of the egg girls. The question was to find the radius of the circle that circumscribes that intersects the points A, B, C, and D. Now this crazy looking professor dude claimed that it was impossible with a zero percent success rate...I immediately pressed X to doubt. The girls said that no such circle exists, but is that really the case? Well I will find the answer to that question.
The full written proof will be found in the following four photos:
Or hopefully this formatting works out and I can directly add the images:
First, as seen in proof part 1 we are given a generic non-representative look at a 4-gon (4-gon is a polygon with 4 sides, aka a quadrilateral) inscribed in a circle and we are given the length of each of the sides of the 4-gon. The length of the sides are: A_B = 7, B_C = 11, C_D = 11, and A_D = 9. This is all the information we need to solve this problem.
Solving this problem requires us to find out 3 things
- Is there a circle that circumscribes points A, B, and C?
- Where is point D located?
- If there is a circle that circumscribes points triangle formed about points A, B, and C, will it also contain point D on the circle's perimeter?
So LET'S GET STARTED!!!!!
First let us establish the coordinate system that we will be working in. The most convenient coordinate system, I believe, is the one centered on point B with the central axes aligning with lines A_B and B_C because A_B and B_C are perpendicular. This makes the coordinates of points A, B and C:
A = (0,7)
B = (0,0)
C = (11,0)
Next we move onto Proof Part 2 where we want to find the circle that intersects points A, B, and C. The stand equation for a circle is as follows:
(x-h)^2 + (y-k)^2 = r^2 (or)--> x^2 - 2hx + h^2 + y^2 - 2ky + y^2 - r^2 = 0 (1)
Where h and k are constants t
... keep reading on reddit ➡I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.
Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.
Do your worst!
I'm surprised it hasn't decade.
For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.
I said "hey look, an escaPEA"
No one near me but it didn't half make me laugh for a good hour or so!
Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂
It really does, I swear!
Because she wanted to see the task manager.
They’re on standbi
Pilot on me!!
Heard they've been doing some shady business.
https://preview.redd.it/iay6s58c48b71.png?width=1043&format=png&auto=webp&s=ccc32b927c7f3ce17a1a30fa5cd5087d09cc95de
