What are the properties of the incenter of a triangle?
5
Practice makes perfect
Besides the lengths of two segments, the question also states that G is the incenter of triangle â–³ ABC. According to the Incenter Theorem, the incenter is equidistant from the sides of the triangle. Let's mark the corresponding congruent segments on the diagram.
We are asked to find EG, but according to the previous observation we can find FG instead. We can do this by focusing on the right triangle â–³ FGC.
In this right triangle the length of the hypotenuse GC=13 and the length of one of the legs CF=12 is given. Using the Pythagorean Theorem, we can find the length of the second leg FG.
