Question

Will someone please help me!!! I don’t know the answer to these! I don’t even know if I did them right!

Answer 1

`BD = 12` units

`AB = 16` units

`FG=√(105)`

`EC=4√(10)` units

`AC=8√(10)` units

Explanation:

A circumcenter is the point where the perpendicular bisectors of a triangle intersect.

This means

• BD = DC;
• BF = FA;
• AE = EC.

Since BC = 24 units, then BD = 12 units (half of BC).

Since FA = 8 units, AB = 16 units (twice FA).

Consider right triangle BGF. In this triangle, BF = 8 units (congruent to FA), BG = 13 units. By the Pythagorean theorem,

`FG^2=BG^2-BF^2\\ \\FG^2=13^2-8^2\\ \\FG^2=169-64=105\\ \\FG=√(105)\ units`

Triangles BFG and AFG are congruent right triangles, then BG = AG. In right triangle AGE,
`GE=3` units,
`AG=13` units. By the Pythagorean theorem,

`AE^2=AG^2-GE^2\\ \\AE^2=13^2-3^2=169-9=160\\ \\AE=√(160)=4√(10)\ units`

`AE = EC=4√(10)\ units`

`AC = 2AE=2\cdot 4√(10)=8√(10)\ units`