In the diagram shown, ΔABC is isosceles with AB = CB. Circle M is inscribed in ΔABC such that it is tangent at points D, E, and F. If the length of BF is twice the length of CF and the perimeter of ΔABC is 32 inches, then determine the length of side BC in inches.

BC = 12 inches

Step-by-step explanation:

As the triangle is isosceles, we have that AE = CF and EB = FB

If we call AE by x, we have that EB = 2x, FB = 2x and CF = x

As E and D are points tangent to the circle, we have that AE = AD = x

As D and F are points tangent to the circle, we have that CD = CF = x

So if the perimeter is 32, we have that:

AE + EB + BF + FC + CD + DA = 32

x + 2x + 2x + x + x + x = 32

8x = 32

x = 4

The length of BC is equal BF + FC = 2x + x = 3x = 12 inches

i believe the correct answer is b.

in the math equation 8 x 7 = 56, the 8 and the 7 are both factors of 56, since in this lesson we will use square tiles to figure out the factors of a whole find as many different arrays as you can, but follow one important rule: all the rows must have the i can make two rows of nine, so 2 and 9 are both factors of 18.

step-by-step explanation: