Let's begin with recalling the Incenter Theorem.
The angle bisectors of a triangle
intersect at a point called the incenter
that is equidistant from the sides of the triangle.
Since we are given that S is the incenter of triangle PLJ, SQ and KS are congruent.
As â–³ JQS is a right triangle, we can use the Pythagorean Theorem to evaluate the length of QJ. According to this theorem, the sum of the squared legs of a right triangle is equal to its squared hypotenuse.
QJ^2+SQ^2=JS^2
In the previous exercise we found that SQ has a length of 6, and we are given that the length of JS is 10. Using this information, we can find the length of QJ.
