Finding the circumcenter of a triangle
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In each of the following cases, find the center of the circle circumscribed about the given triangle. 1° Triangle ABC 2° Triangle IFL 3° Triangle RON
This question includes visual content: The image displays three separate triangles labeled for a geometry construction task. 1) Triangle ABC (acute, blue lines). 2) Triangle IFL (obtuse, red lines) with partial arc construction lines visible above it. 3) Right-angled triangle RON (green lines, with a right angle mark at O).
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Hi Matjar., let's learn how to find the circumcenter of different types of triangles by looking at these three examples.
Finding the Circumcenter of a Triangle
Recall that the center of a circumscribed circle, or the circumcenter, is the point where the perpendicular bisectors of the triangle's sides intersect.
Let's start with the first case, triangle A B C, which appears to be an acute triangle.
Case 1: Acute Triangle ABC
For an acute triangle, we draw the perpendicular bisectors for at least two sides. Notice how they meet at a point inside the triangle.
So, for an acute triangle, the center lies inside the triangle.
Next, let's look at case two, triangle I F L, which is an obtuse triangle.
Case 2: Obtuse Triangle IFL
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