Question

Given:• Points A, B, and C are points of tangency.• VZ = 24• AV = 14• The perimeter of AWV Z is 64.BzАсwFind AW.281416O

Answer 1

A circle is inscribed in a triangle touching points A, B and C.

Thus,

Side AV = Side BV;

Side BZ = Side CZ;

Side AW = Side CW.

`\begin{gathered} \textAV \\ \textVZ \\ |BZ|=24-14 \\ |BZ|=10,\text then \\ \text= \end{gathered}`

Then, using the perimeter to get the unknown, we have;

`\begin{gathered} P=|AV|+|AW|+|VZ|+|CZ|+|CW| \\ 64=14+x+24+10+x \\ 2x=64-48 \\ 2x=16 \\ x=(16)/(2) \\ x=8 \end{gathered}`

Thus, |AW| is 8