Andelko measured the largest chord on his slice of pizza, and found it was 20 cm long. From the midpoint of the chord to the outside of the pizza, the shortest distance was 2 cm. What was the diameter of the pizza?
52
To find the diameter of the pizza, we can use the relationship between the diameter and the chord of a circle. The shortest distance from the midpoint of the chord to the outside of the pizza is called the radius.
Given that the shortest distance (radius) is 2 cm, we can determine the diameter by doubling this value.
So, the diameter of the pizza is 2 * 2 cm = 4 cm.
To determine the diameter of the pizza, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, we can consider the chord on the pizza as the base of a right triangle, and the shortest distance from the midpoint of the chord to the outside of the pizza as the height.
Let's denote the length of the chord as c, the shortest distance as h, and the diameter of the pizza as d.
According to the Pythagorean theorem, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (h and half of the diameter, which is d/2):
c^2 = h^2 + (d/2)^2
Plugging in the values from the information given in the question:
20^2 = 2^2 + (d/2)^2
Simplifying:
400 = 4 + (d/2)^2
396 = (d/2)^2
Taking the square root of both sides:
√396 = d/2
Since the square root of 396 is approximately 19.89, we can solve for d:
19.89 = d/2
Multiplying both sides by 2:
19.89 * 2 = d
Therefore, the diameter of the pizza is approximately 39.78 cm.
I hope you made a diagram
Let the radius be x
then the distance from the centre of the chord to the centre of the circle is x-2 and we have a right-angled triangle
x^2 = (x-2)^2 + 10^
x^2 = x^2 - 4x + 4 + 100
4x = 104
x = 26
so the diameter is 52 cm