Let ∆ABC be a triangle with circumcenter O, centroid G, and orthocenter H. Let ϕ be a similarity. Show that the triangle ϕ(∆ABC) = ∆ϕ(A)ϕ(B)ϕ(C) has...
(a) circumcenter ϕ(O). (b) centroid ϕ(G). (c) orthocenter ϕ(H)
Let ∆ABC be a triangle with circumcenter O, centroid G, and orthocenter H. Let ϕ be...
the following theorems may be used to answer the question below: power if the point, law if cosines, extended law of sines, incenter, excenter, orthocenter, and circumcenter. Note that the distance between O to A is 5.5cm, G to O is 1.8 cm and G to A is 6.1cm 6, Below you are given the vertex A, centroid G, and the circumcenter O of △ABC. Construct the other two vertices B and C ●A 6, Below you are given the...
Through Geogebra (or any other geometry application): Start with three arbitrary points, O, G, and A.Construct points B and C so that O becomes the circumcenter of triangle ABC and G is the centroid.
the following theorems may be used to answer the question below: power if the point, law if cosines, extended law of sines, incenter, excenter, orthocenter, and circumcenter. Note that the distance between O to A is 5.5cm, G to O is 1.8 cm and G to A is 6.1cm 6, Below you are given the vertex A, centroid G, and the circumcenter O of △ABC. Construct the other two vertices B and C ●A
Let traingle ABC have midpoint B' on AC, C' midpoint of AB and G be centroid. If AC=5, AB=5, and CC'=6 find BC.
Let H be the orthocenter of a nondegenerate... 14. Let H be the orthocenter of a nondegenerate & ABC. Prove that the second point of intersection of two circles with diameters (AH] and [BH] lies on the line (AB).
Given a triangle ABC, let l_1 be the angle bisector of <A and let l_2 be the perpendicular bisector of line BC. Assuming AB > AC, show that l_1 intersection l_2 is not in triangle ABC Excuse l_2 is the perpendicular bisector of line BC hence the right angle. The questions is to show a step by step proof that when l_1 abd l_2 intersect, it will be outside of the given triangle. Given a triangle ABe, let Libe the...
Let G be a group of order 231 = 3 · 7 · 11. Let H, K and N denote sylow 3,7 and 11-subgroups of G, respectively. a) Prove that K, N are both proper subsets of G. b) Prove that G = HKN. c) Prove that N ≤ Z(G). (you may find below problem useful). a): <|/ is a normal subgroup, i.e. K,N are normal subgroups of G (below problem): Let G be a group, with H ≤ G...
13. Let I be the incenter of a triangle ABC. If <ABC 270 find & AIC. 5 Hint: Be careful with the signs of angles
3 8 16 (0 complete) This Q Plot each point and form the triangle ABC. Show that the triangle ABC is a right triangle. Find its area. A (-2,11); B (5,7); C ( 1,0) Choose the correct graph below that shows points A, B, C, and triangle ABC. O A. O B. O C. OD. -14 14 Ha Show that the triangle ABC is a right triangle. Select the correct choice below and fill in the answer boxes to complete...
2. Consider a triangle ABC. Let M denote the midpoint of side AC. If BM - AM, show that angle B is a right angle. (10 points)