When Is a Quadrilateral Cyclic?
Read this topicExplanations 8
- There are several fundamental criteria that help determine if a quadrilateral is cyclic. First, a quadrilateral is cyclic iff opposite angles sum to 180∘180^\circ180∘. This is b…
By Vincent Huang, David Altizio, Darshan Chakrabarti, Victor Wang, Moor Xu
- When does a Quadrilateral become Cyclic?(Incomplete) Fundamental definition: A quadrilateral ABCDABCDABCD is cyclic\textbf{cyclic}cyclic if there is a circle passing through fou…
By Devarsh Ruparelia, Amber Li, Victor Wang
- Ancient mathematicians were fascinated with geometric coincidences. Let's get a feel for this ourselves. I drew a triangle in the sand, and noticed that it was possible to draw …
By Po-Shen Loh, Freya Edholm, Tom Shen
- When is a quadrilateral cyclic? In general, a polygon is cyclic if there exists a circle passing through all the vertices of the polygon. So, before we look at quadrilateral, le…
By Zi Song Yeoh, Alex Federspiel
- Let's take this video and add even more life. This person is very enthusiastic! (There is still a gap here to contribute to!)
By Po-Shen Loh
- Let ABCABCABC be a triangle, and D,E,FD, E, FD,E,F lie on BC,AC,ABBC, AC, ABBC,AC,AB respectively. Let ⊙AEF\odot AEF⊙AEF and ⊙BDF\odot BDF⊙BDF intersect at PPP. We're going to s…
By Yang Liu, Expii Team
- Quadricyclicity given side lengths? Here's one you might have to think about for a while: Also, so either way, let's assume there is such a construction. If we didn't know the a…
By Ahaan Rungta, Alex Federspiel
- কোন চতুর্ভুজের শীর্ষবিন্দু ৪টি দিয়ে একটি বৃত্ত আঁকা গেলে সেই চতুর্ভুজকে বৃত্তস্থ চতুর্ভুজ বলে। বৃত্তস্থ চতুর্ভুজ নিয়ে কথা বলার আগে ত্রিভুজ নিয়ে কিছু বলি। তাহলে কী চতুর্ভুজের ক্ষ…
By Ittihad Ahmed, Adib Hasan · বাংলা
Problems 8
- Is it cyclic?
- A cyclic quadrilateral is:
- Does it have to be cyclic?
- Is there always a cyclic quadrilateral whose side lengths are aaa, bbb, ccc, and ddd, in that order?
- Quadrilateral ABCDABCDABCD is cyclic, and angle AAA measures 95 degrees. What is the measure of angle CCC?
- Problem! As David showed before, right angles create cyclic quads. Let ABCABCABC be a right triangle, where K,L,K, L,K,L, and MMM are the feet of the AAA-, BBB-, and CCC-heights…
- In triangle ABCABCABC, AB=28AB = 28AB=28, AC=36AC = 36AC=36, and BC=32BC = 32BC=32. Let DDD be the point on segment BCBCBC satisfying ∠BAD=∠DAC\angle BAD = \angle DAC∠BAD=∠DAC, …
- What is the measure of the angle indicated by the question mark, if the angles marked aaa have measure aaa degrees, and the angles marked ccc have measure ccc degrees?