Flashcards on Centroid, orthocenter, circumcircle and incircle
Centroid, Orthocenter, Circumcenter, Incircle Explained
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Triangle Centers and Associated Circles
8 cards
Card 1
Question: What is a median of a triangle?
Answer: A line segment joining a vertex to the midpoint of the opposite side.
Card 2
Question: How many medians does every triangle have?
Answer: Three, one from each vertex.
Card 3
Question: What is the point of concurrency of the three medians of a triangle called?
Answer: The centroid (often denoted by G).
Card 4
Question: What is the centroid also known as in relation to a triangle?
Answer: The geometric center or center of mass/balance point if the triangle were a thin, uniform plate.
Card 5
Question: In what ratio does the centroid divide each median?
Answer: In a 2:1 ratio, with the longer segment from the vertex to the centroid and the shorter segment from the centroid to the midpoint of the side.
Card 6
Question: Does the centroid always lie inside the triangle?
Answer: Yes.
Card 7
Question: How are the coordinates of the centroid G(x_G, y_G) calculated if the vertices of a triangle are A(x_A, y_A), B(x_B, y_B), and C(x_C, y_C)?
Answer: x_G = (x_A + x_B + x_C) / 3 and y_G = (y_A + y_B + y_C) / 3
Card 8
Question: What is a common misconception about the centroid?
Answer: Students sometimes confuse it with other centers or assume it's always at the geometric center of the triangle's bounding box; it's specifically the c