Question

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 =

Answer 1

Answer:7 and 6

Step-by-step explanation:

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Answer 2

Part a)

we know that

The incenter is the point forming the origin of a circle inscribed inside the triangle

so

in this problem

The radius of the inscribed circle is equal to $24\ units$

so

$3x+3=24$

solve for x

$3x=24-3$

$x=21/3$

$x=7\ units$

therefore

the answer Part a) is

$x=7\ units$

Part b)

we know that

The circumcenter is the center of the the circle that passes through all three of the triangle's vertices

so

In this problem

The radius of the circle is equal to $26\ units$

$5x-4=26$

solve for x

$5x=26+4$

$x=30/5$

$x=6\ units$

therefore

the answer Part b) is

$x=6\ units$