The radius of the inscribed circle is 6 cm. What is the number of centimeters in the length of line AB? Express your answer in simplest radical form.

SydSu22 Apr 9, 2019

#1**+2 **

Use your knowledge on special triangles (especially 30, 60, 90)

Also use this diagram to help:

Try to find the side length of the square then use special triangle rule to find the bottom side of the triangle, this will lead you to the length of BC.

CalculatorUser Apr 9, 2019

#3**+2 **

Thanks, CU!!!

Using CU's diagram.....

BF = 6 and angle FPC = 75°

tan FPC = FC /PF

tan 75 = FC / 6

6tan 75 = FC

6 tan (45 + 30) = FC

FC = 6 [ tan 45 + tan 30 ] / [ 1 - tan45*tan30]

FC = 6[ 1 + √3/3] / [ 1 - 1*√3/3]

FC = 6 [ 3 + √3] / [ 3 - √3]

FC = 6[9 + 6√3 + 3 ] / [ 9 - 3]

FC = 6 [ 12 + 6√3 ] / [ 6]

FC = [ 12 + 6√3 ]

So....BF + FC = 6 + [ 12 + 6√3] = 18 + 6√3 = BC

So AB = (2/√3)BC = (2/√3) [ 18 + 6√3] = 36/√3 + 12 = 12√3 + 12

CPhill Apr 10, 2019