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

Answer:

$BD = 12$ units

$AB = 16$ units

$FG=\sqrt{105}$

$EC=4\sqrt{10}$ units

$AC=8\sqrt{10}$ units

Step-by-step 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,

$FG^2=BG^2-BF^2\\ \\FG^2=13^2-8^2\\ \\FG^2=169-64=105\\ \\FG=\sqrt{105}\ units$

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,

$AE^2=AG^2-GE^2\\ \\AE^2=13^2-3^2=169-9=160\\ \\AE=\sqrt{160}=4\sqrt{10}\ units$

$AE = EC=4\sqrt{10}\ units$

$AC = 2AE=2\cdot 4\sqrt{10}=8\sqrt{10}\ units$