categories: informational / mathematics
I won't ramble on too much in this post 🙂 Besides, mathematics doesn't require that at all. You don't need any lofty words to convey it. That said, you can love it, or you can hate it. Personally, I love it, and I want to share that love with you.
I have prepared a few interesting exercises for you from the extended matura exam, from the Planimetry chapter, which is the branch of mathematics dealing with the study of figures on a plane. For now I won't say exactly which plane I mean, since I don't want to overwhelm you with an excessive dose of knowledge right at the start (and everyone intuitively understands the concept of a plane anyway) 🙂 Everything has its time.
Exercise 1
The angle bisectors of a cyclic quadrilateral ABCD intersect at four different points: P, Q, R, S. Your task is to show that a circle can be circumscribed around PQRS.Exercise 2
In triangle ABC, the interior angle at vertex A measures 50 degrees, and the interior angle at vertex C measures 60 degrees. Circle "O1" passes through A and intersects sides AB and AC of triangle ABC at points D and E, respectively. Circle "O2" passes through B and intersects circle "O1" at point D and at point F, which lies inside triangle ABC (F only). Furthermore, O2 intersects side BC of the triangle at point G. Prove that a circle can be circumscribed around quadrilateral CEFG.If you'd like to see the solutions to these exercises, I invite you to visit this subpage containing the ready-made solutions to the given problems 🙂 Keep in mind, however, that you will grow the most by solving these exercises yourself!
Solutions
