Question

AABC is shown below. GE = -3y + 18 and GF = 5y + 2.
E
B
F
Find the measure of the radius of the inscribed circle of AABC.
Radius =

Answer 1

Answer:

Radius = 12

Step-by-step explanation:

For an inscribed circle of a triangle ABC,

GE = GF = GD = radius of the inscribed circle

Therefore, (-3y + 18) = (5y + 2)

-3y + 18 - 5y = 5y + 2 - 5y

-8y + 18 = 2

-8y + 18 - 18 = 2 - 18

-8y = -16

8y = 16

$\frac{8y}{8}=\frac{16}{8}$

y = 2

Therefore, GE = -3y + 18

                       = -3(2) + 18

                       = -6 + 18

                       = 12

Radius of the inscribed circle = GE = 12 units

Answer 2

The measure of the radius of the inscribed circle is 12 units

From the given diagram, GE = GF

Given the following parameters:

GE = -3y + 18 and:

GF = 5y + 2

Equating both expressions

-3y + 18 = 5y + 2

-3y - 5y = 2 - 18

-8y = -16

y = 16/8

y = 2

The measure of the radius of the inscribed circle is GE

GE = -3y  + 18

GE = -3(2) + 18

GE = -6 + 18

GE = 12 units

Hence the measure of the radius of the inscribed circle is 12 units

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