MATH SOLVE

5 months ago

Q:
# The triangle has a point of concurrency at P. Find the value of x that would make P the incenter of the triangle. x = Find the value of x that would make P the circumcenter of the triangle. x =

Accepted Solution

A:

Part a) we know thatThe incenter is the point forming the origin of a circle inscribed inside the trianglesoin this problemThe radius of the inscribed circle is equal to [tex]24\ units[/tex]so[tex]3x+3=24[/tex]solve for x[tex]3x=24-3[/tex][tex]x=21/3[/tex][tex]x=7\ units[/tex]thereforethe answer Part a) is [tex]x=7\ units[/tex]Part b) we know thatThe circumcenter is the center of the the circle that passes through all three of the triangle's verticessoIn this problemThe radius of the circle is equal to [tex]26\ units[/tex][tex]5x-4=26[/tex]solve for x[tex]5x=26+4[/tex][tex]x=30/5[/tex] [tex]x=6\ units[/tex]thereforethe answer Part b) is [tex]x=6\ units[/tex]