Answer:
No
Step-by-step explanation:
To determine if the second longest side of the triangle is tangent, or at a right angle to the circumference of the circle, we have to determine if the triangle is a right triangle using the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
where [tex]c[/tex] is the longest side (the hypotenuse).
Plugging in the given side lengths, we get:
[tex]3^2 + 9^2 \stackrel{?}{=} 12^2[/tex]
[tex]9 + 81 \stackrel{?}{=} 144[/tex]
[tex]90 \ne 144[/tex]
Since Pythagorean's Theorem is not satisfied, the triangle is NOT a right triangle. Thus, its second longest side is NOT tangent to the circle's circumference.
