A belt wrapped tightly around cicle O forms a 60 degree angle at P, a point outside the circle. Find the length of the belt if cicle O has a radius of 9.
That's kind of hard to imagine, but it seems to me you just plug 9 in into the formula... Please clarify if I'm wrong.
A belt wrapped tightly around cicle O forms a 60 degree angle at P, a point outside the cicle. Find the length of the belt if the cicle O has a radius of 9.
diagram looks like a cicle with two tangent lines joining at point P outside the cicle. looks like a ice cream cone.
need help
Lines from the points of contact of a tangent to the center of the circle are at right angles to the tangent.
Draw triangles connecting a tangent point, P and the center of the circle. This will form two 30-60-90 right triangles.
The angle subtended by the belt from the center of the circle is 120 degrees.
The length of the belt is (2/3)*pi*R
= 18.85
To find the length of the belt, we can start by visualizing the given information.
We have circle O with a radius of 9 units. Let's draw the circle and label the center as O.
We are also given that the belt wrapped tightly around the circle forms a 60 degree angle at point P, which is located outside the circle. Let's mark point P on the same side of the center as the angle.
To find the length of the belt, we need to find the distance that the belt covers along the circumference of the circle.
Since we know the radius of the circle is 9 units, we can use the formula for the circumference of a circle to find this distance.
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
Plugging in the given radius of 9 units, we get:
C = 2π(9) = 18π
Now we need to determine the proportion of the circumference that the belt covers.
We know that the angle at P is 60 degrees. Since the total angle in a circle is 360 degrees, we can set up a proportion to find the proportion of the circumference covered by the belt.
Let x represent the length of the belt.
60 degrees is to 360 degrees as x is to the total circumference (18π):
60/360 = x / (18π)
Simplifying this proportion, we get:
1/6 = x / (18π)
To find the value of x, we can cross-multiply:
6 * x = 18π
Dividing both sides by 6, we get:
x = 3π
Therefore, the length of the belt wrapped tightly around circle O is 3π units.