To calculate the corresponding values for the triangle in the larger circle, we need to use the fact that all circles are similar. This means that the corresponding sides of the circles are proportional, and their corresponding angles are congruent. We can use this property to find the missing values.
First, let's find the radius of circle B. Since the ratio of the corresponding sides of the circles is 4.25, we can find the radius of circle B as follows:
R_B = 4.25 * R_A = 4.25 * 2.9 = 12.33 cm
Now, we can use the radius of circle B to find the lengths of the sides of triangle BSH. Since triangle BSH is also similar to triangle AOG, we can use the same ratio of 4.25 to find the lengths of the corresponding sides. We have:
BS = 4.25 * OA = 4.25 * 3.2 = 13.6 cm
BH = 4.25 * OG = 4.25 * 2.6 = 11.05 cm
To find the length of SH, we can use the fact that the sum of the lengths of the sides of a triangle is equal to its perimeter. We have:
Perimeter of triangle BSH = BS + SH + BH = 13.6 + SH + 11.05 = 24.65 cm
Therefore, the perimeter of triangle BSH is 24.65 cm.
To find the measure of angle LSBH, we can use the fact that the corresponding angles of similar triangles are congruent. Since angle AOG is a right angle, we know that angle BSH is also a right angle. Therefore, we have:
angle LSBH = angle BSH - angle LBS = 90 - 64 = 26 degrees
Therefore, the measure of angle LSBH is 26 degrees.
To find the area of triangle BSH, we can use Heron's formula, which gives the area of a triangle in terms of its side lengths. We have:
s = (BS + SH + BH)/2 = 24.65/2 = 12.325 cm
Area of triangle BSH = sqrt(s(s-BS)(s-SH)(s-BH)) = sqrt(12.3250.0251.275*0.075) = 0.167 cm^2
Therefore, the area of triangle BSH is 0.167 cm^2.
To find the length of the circumference of circle B, we can use the formula for the circumference of a circle, which is given by:
C_B = 2piR_B = 2pi12.33 = 77.42 cm
Therefore, the length of the circumference of circle B is approximately 77.42 cm.
