Question

The perpendicular bisectors of AABC intersect at point G and are shown in blue. Find GA. G A 7 D GA=

F 11 -9- B E с​

Answer 1

The length of GA for the right triangle GDA with where GD is a perpendicular bisector for ∆ABC is equal to √89.

A perpendicular bisector is a line or segment that cuts another line segment into two equal parts at a right angle. Given that GF and GD are perpendicular bisector of ∆ABC, then GF is equal to GD, also ∆GFC and ∆GDA are right triangles, so

For ∆GFC by Pythagoras; GF = √(11² - 9²)

GF = √40

Also for ∆GDA, we can evaluate for GA as follows;

GA = √[(√40)² + 7²]

GA = √(40 + 49)

GA = √89

Therefore, we have the value of the length for GA derived to be √89 or 9.4 to the nearest tenth.