SOLUTION: A diagram shows the design of an earring The earring consists of a circle inside an equilateral triangle The sides of the triangle are tangents to the circle The radius of the c

Algebra ->  Circles -> SOLUTION: A diagram shows the design of an earring The earring consists of a circle inside an equilateral triangle The sides of the triangle are tangents to the circle The radius of the c      Log On


   



Question 929594: A diagram shows the design of an earring
The earring consists of a circle inside an equilateral triangle
The sides of the triangle are tangents to the circle
The radius of the circle is 8mm
The distance from the centre of the circle to each vertex of the triangle is 17mm
Calculate the perimeter of the triangle

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The distance from the center of the circle to the vertex of the triangle (Y) forms a right triangle along with the radius of the circle (R). The other leg of that triangle is 1/2 the length of the equilateral triangle leg, X.
X%5E2%2BR%5E2=Y%5E2
X%5E2%2B8%5E2=17%5E2
X%5E2=289-64
X%5E2=225
X=15
So the perimeter would be,
P=3%282X%29
P=6%2815%29
P=90cm