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3 votes
in triangle ABC, point E (5, 1.5) is the circumcenter, point He (4.3, 2.3) is the incente, and point I (3.6, 2.6) is the centroid.what is the approximate length of the radius that circumscribes triangle ABC?

in triangle ABC, point E (5, 1.5) is the circumcenter, point He (4.3, 2.3) is the-example-1
User Amen
by
7.2k points

1 Answer

3 votes

1) Gathering the data

E (5,1.5) Circumcenter

H (4.3,2.3) incenter

I (3.6, 2.6) is the centroid.

2) Examining the figure we can see point C and B as the vertices of the

triangle, to find the radius let's use the distance formula between point E and C

E(5, 1.5) and C(3,5)


\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)}^2 \\ \\ d=\sqrt[]{(5-3_{})^2+(1.5_{}-2.6_{})}^2 \\ d=2.28 \end{gathered}

Since the radius is a line segment from the origin to the circumference then the distance BC = radius of the circumscribed triangle

Radius = 2.28

User Mhavel
by
6.4k points
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