A 60 degree arc, of circle A, has exactly the same lenght as a 45 degree arc, of circle B. Find the ratio of the radius of circle A to the radius of circle B
i think the answer is 3/4??
correct
To find the ratio of the radius of circle A to the radius of circle B, we can use the formula for the circumference of a circle. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
Let's denote the radius of circle A as rA and the radius of circle B as rB. We know that the length of a 60-degree arc in circle A is equal to the length of a 45-degree arc in circle B.
The length of an arc is determined by the fraction of the circumference that it subtends. Therefore, the lengths of the 60-degree and 45-degree arcs can be expressed as a fraction of the respective circle's circumference.
For circle A, the length of the 60-degree arc can be calculated as:
Length of 60-degree arc in circle A = (60/360) * Circumference of circle A
Length of 60-degree arc in circle A = (1/6) * 2πrA
Similarly, for circle B, the length of the 45-degree arc can be calculated as:
Length of 45-degree arc in circle B = (45/360) * Circumference of circle B
Length of 45-degree arc in circle B = (1/8) * 2πrB
Since we're given that the lengths of these two arcs are equal, we can set up an equation:
(1/6) * 2πrA = (1/8) * 2πrB
Simplifying the equation, we can cancel out common factors:
rA = (6/8) * rB
rA = (3/4) * rB
Therefore, the ratio of the radius of circle A to the radius of circle B is 3:4.