The image of the inscribed circle is missing so i have attached it.
Answer:
x = 35
None of the given options are correct.
Thus, Option D is the answer.
Step-by-step explanation:
From the attached image, we can see that there are two lines projecting out of the centre of the circle with one having it's endpoint touching the edge of the hexagon while the other is perpendicular to the centre of a side of the hexagon and labeled x has it's endpoint touching both the circumference and the hexagon side.
Since line labeled x projects from the centre of the circle to the circumference, we can say that the radius is x.
The triangle formed is a right angled triangle with the other part touching only the hexagon as the hypotenuse.
We see the remaining part between the circle and the hexagon of this hypotenuse line given as 2.
Thus, hypotenuse = x + 2
This is because from the centre to the circumference is x as earlier discussed and this hypotenuse line crosses the circumference of the circle before touching the edge of the hexagon.
Using pythagoras theorem, we can find x:
x² + 12² = (x + 2)²
x² + 144 = x² + 4x + 4
x² will cancel out to give;
4x + 4 = 144
4x = 144 - 4
4x = 140
x = 140/4
x = 35
