a Recall that if two segments from the same exterior point are tangent to a circle, then they are congruent.
B
b Add all of the side lengths of the given triangle.
A
a x=4
B
b P=52
Practice makes perfect
a We are given that triangle JKL is circumscribed about ∘ R. Let's look at the given diagram.
Now recall that if two segments from the same exterior point are tangent to a circle they are congruent. This means that OL=NL.
OL=NL
x+3= 4x-9
Let's solve the equation using inverse operations.
b In this part we want to evaluate the perimeter of △ JKL. To do this we need to know all of the side lengths of this triangle.
First, let's evaluate OL and NL using the fact that they are equal and x=4.
OL=NL=4+3=7
These segments have a length of 7. Let's add this information to our picture.
Again let's recall that if two segments from the same exterior point are tangent to a circle, then they are congruent. Therefore JM=JO and KM=KN.
Finally, we can evaluate the perimeter by adding all of the side lengths. Notice that we will rewrite each side length as a sum using the Segment Addition Postulate.
P=JK+KL+JL ⇓
P=( 12+ 7)+( 7+ 7)+( 12+ 7)
Let's evaluate the above sum.
