Find the perimeter of figure GHI. Assume that segments that appear to be tangent are tangent.

Question

se any relevant academic vocabulary.

 

 

Answer 1

The lengths of the tangents drawn from an external point to the circle are equal in length.

So HJ=HK

7x+4=13x-8

6x=12

x=2

HJ=7x+4=7(2)+4=18

HK=18

LI=KI=15

GI=52

GL=GI-LI=52-15= 37

GL=GJ=37

Perimeter of GHI= sum of all the sides=GJ+JH+HK+KI+GI=37+18+18+15+52=140

Answer 2

7x + 4 = 13x - 8; 6x = 12; x = 2; GL = 52 - 15 = 37; HJ = 7·2 + 4 = 18

Perimeter P = 2(HJ + GL +KI) =2(18 + 37 + 15) = 140