Question

G is the circumcenter of triangle ACE.
Find AE to the nearest tenth.

Answer 1

Since G is the circumcenter of triangle ACE, the length of AE to the nearest tenth is 18.6 units.

In Mathematics and Euclidean Geometry, a circumcenter is the point where perpendicular bisectors (right-angled lines to the midpoint) of the sides of a triangle meet together or intersect.

Next, we would determine the length of segment A F by applying Pythagorean theorem;

`AG^2 =A\;F^2+GF^2\\\\A\;F^2=AG^2-GF^2\\\\A\;F^2=11.2^2-6.1^2\\\\A\;F^2=125.44-37.21\\\\A\;F=√(88.23)`

A F = 9.4 units.

Since GF represents a perpendicular bisector, segment A F must be equal to segment EF;

A F = EF

For the length of segment AE, we have;

AE = A F + EF

AE = 9.4 + 9.4

AE = 18.6 units.