If AXYZ has the same circumcircle and the same orthocentre as AABC, prove that the nine-point...
Prove that the circumcircle of AABC is the nine-point circle of A1.11.
25. Suppose that AABC is equilateral. Prove that the area of its circumcircle is four times the area of its incircle.
can you please please help me with these proofs
R Cand CoDNder the triangle AABC and M and NIwopaints such thatM PrOve that MEMAN kBA) M MBC)m ACRI. Let AABC be a triangle with AB< AC and let D be a point such that A C - D. Show that for every point M with B- M- C we have m(< ABM) +m(< BMA)> m(< CMD)+m(< MDC) Prove that if in the triangle AABC the altitudes AD and BE (where...
TIPS 1. Given AABC and the midpoints D, E and F of the sides as shown, prove that for any point O located on, in or outside the triangle that: OD+OE+OF = OA+OB+OC You must use vectors methods.
Task: Write a Java program to implement a simple graph editor that can be used to draw a circumcircle. The editor has a pull-down menu on top of the screen with 2 buttons: "Circumcircle" and "Quit". 1) When the user selects "Circumcircle", he/she can draw a circumcircle on the screen as described in Exercise 2.6 on page 59 of the textbook. 2) The editor terminates/quits execution if the user selects "Quit" from the pull- down menu. 3) The editor has...
Prove that the three perpendiculars in a triangle cross through the same point Hint: Construct the two perpendiculars from A and B and label their intersection point as O. Then prove that vector OB is perpendicular to vector AB
GEOMETRY Exam 9-Continued Student Number Student's Name 17. The vertices of AABC are A(-1, 1), B(0, 3), and C(3,4). Graph the image of AABC after a composition of the following transformations in the order they are listed. B A. Translation: (x. y)(x-3,y- 3) Reflection: in the line y x Is the composition a glide reflection? Yes No Yes Is the image the same if the order of the transformations is switched? (reflection, then glide) No 18. The vertices of AABC...
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X,...
#3 please
Isometries 1. (Apt) Prove that the composition of two isometries is an isometry. 2.4pt) Prove that if F and G is an isometry of the plane and F(AABC) = G(AABC) = AA'B'C', then F = G. That is, an isometry is uniquely determined by three non-collinear points (a triangle) and their images. Consider using an inverse of one of the isometries. 3. (4pt) To prove that a reflection, Rom, is an isometry, it must be shown that it...
7. State and prove the Law of Sines for triangles in Euclidean geometry. 8. Assume Euclidean geometry. Fix a circle and let AB and CD be two chords of the circle that intersect at point P. Prove that AP × PB = CP × PD (one both sides of the equation you are multiplying the lengths)
7. State and prove the Law of Sines for triangles in Euclidean geometry. 8. Assume Euclidean geometry. Fix a circle and let AB and...