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n200080 [17]
3 years ago
12

Point G is the centroid of the right △ABC with hypotenuse AB=18 in. Find CG.

Mathematics
2 answers:
natita [175]3 years ago
5 0
<h3>Answer:</h3>

6 in

<h3>Explanation:</h3>

CG is 2/3 the length of median CM, where M is the midpoint of AB. M is the center of the circumscribing circle, which has radius 9 in, so CM is 9 in, and CG is 6 in.

Virty [35]3 years ago
4 0

Answer:

CG = 6 in.

Step-by-step explanation:

Given information : Point G is the centroid of the right △ABC with hypotenuse AB=18 in.

We know that circumcenter of a right angle triangle is the midpoint of the hypotenuse.

Let point M be the circumcenter of △ABC.

Hypotenuse AB=18 in.

Radius of circumcircle = \frac{18}{2}=9 in.

Know connect the circumcenter M with the vertex C. CM is a median of the △ABC from vertex C.

MC = radius of the circumcircle = 9 in.

We know that centroid divides each median in a ratio of 2:1.

Point G is the centroid of the right △ABC. It means point G divides CM median in a ratio of 2:1.

CG=9\times \frac{2}{3}=6

GM=9\times \frac{1}{3}=3

Therefore, the measure of CG is 6 in.

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