Answer:30.73cm
Explanation:
Since the circle with center B and radius 9 cm passes through points A and C, it follows that AB and BC are both radii of the circle. Therefore, AB = BC = 9 cm.
To find the length of AC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Since we know that AB = BC = 9 cm, and we can see from the diagram that angle ABC is a right angle, we have:
AC^2 = AB^2 + BC^2
AC^2 = 9^2 + 9^2
AC^2 = 162
AC = sqrt(162) = 12.73 (rounded to two decimal places)
Therefore, the perimeter of ABC is:
AB + BC + AC = 9 + 9 + 12.73 = 30.73 cm (rounded to two decimal places).