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Deffense [45]
2 years ago
14

Triangle ABC is isosceles with AB=CB. Circle M is inscribed in Triangle ABC such that it is tangent at points D, E, and F. If th

e length of BF is twice the length of CF and the perimeter of Triangle ABC is 32 inches, then determine the length of side BC in inches.
Mathematics
1 answer:
Ierofanga [76]2 years ago
8 0

Answer:

The answer is "12 inches".

Step-by-step explanation:

Please find the image file of the graph.

We know AE = CF \ and \ EB = FB so because the triangle is isosceles.

EB = 2x, FB = 2x,\ and \ CF = x when AE is called by x.

We know that AE = AD = x since E and D are tangent points to a circle.

They have CD = CF = x since D and F are tangent points only to circle.

Thus, if the perimeter is 32, the following is the result:

\to AE + EB + BF + FC + CD + DA = 32\\\\\to x + 2x + 2x + x + x + x = 32\\\\\to 8x = 32\\\\\to x = 4

Therefore the length of BC = BF + FC = 2x + x = 3x = 12\  inches

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