Question

If G is the circumcenter of triangle ACE, find GD

Answer 1

Answer:22.6

Explanation:

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Answer 2

`GD=16√(2)\ units`

Explanation:

we know that

The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter (point G)

The circumcenter is equidistant from the vertices of the triangle

so

AG=CG=EG

step 1

Find the value of x

AG=CG

substitute the given values

`7x-41=5x-19`

solve for x

`7x--5x=41-19`

`2x=22`

`x=11`

step 2

Find the length side DC

we know that

DC=DE

Because GD is a perpendicular bisector

so

`DC=28\ units`

step 3

Find the length side GD

In the right triangle GCD

Applying the Pythagorean Theorem

`CG^2=GD^2+DC^2`

we have

`DC=28\ units`

`CG=5x-19=5(11)-19=36\ units`

substitute the values

`36^2=GD^2+28^2`

`GD^2=36^2-28^2`

`GD^2=512`

`GD=√(512)\ units`

simplify

`GD=16√(2)\ units`