1) Find the circumference of a circle in which a \(50\) cm chord is \(70\) cm from the center.
2) Find the length of \(\overset{\Huge{\frown}}{AB}\) in \(\bigodot O\).
2) Find the length of \(\overset{\Huge{\frown}}{AB}\) in \(\bigodot O\).
3) a) Find the length of a chord that cuts off an arc of measure \(60^{\circ}\) in a circle with radius \(7\).
b) Find the length of a chord that cuts off an arc of measure \(120^{\circ}\) in a circle with radius \(7\).
4) An equilateral triangle is inscribed in a circle of radius \(17\). Find the length of the arc cut by one side of the triangle.
5) A pirate ship at the amusement park swings back and forth like a pendulum. It is mounted on a boom that suspends the ship \(30\) feet from its pivot point. When the ship swings, its center makes a \(150^{\circ}\) arc. If a “ride” is measured as \(10\) complete swings, how far does a person seated in the middle of the ship ride? Assume a complete swing is from extreme to the other and back to the starting point.
b) Find the length of a chord that cuts off an arc of measure \(120^{\circ}\) in a circle with radius \(7\).
4) An equilateral triangle is inscribed in a circle of radius \(17\). Find the length of the arc cut by one side of the triangle.
5) A pirate ship at the amusement park swings back and forth like a pendulum. It is mounted on a boom that suspends the ship \(30\) feet from its pivot point. When the ship swings, its center makes a \(150^{\circ}\) arc. If a “ride” is measured as \(10\) complete swings, how far does a person seated in the middle of the ship ride? Assume a complete swing is from extreme to the other and back to the starting point.
6) A certain machine is to contain two wheels, one of radius \(3\) cm and one of radius \(5\) cm, whose centers are attached to points \(14\) cm apart. The manufacturer of this machine needs to produce a belt that will fit snugly around the two wheels, as shown in the diagram below. How long should the belt be?