Points Q and R lie on a circle with center P . The radius of this circle is 9 inches.

Question

Points Q and R lie on a circle with center P . The radius of this circle is 9 inches. Triangle P Q R has a perimeter of 31 inches. What is the length, in inches, of Q R &#175; ?

Accepted Answer

Choice B is correct. Since it's given that P is the center of a circle with a radius of 9 inches, and that points Q and R lie on that circle, it follows that P Q &macr; and R P &macr; of triangle P Q R each have a length of 9 inches. Let the length of Q R &macr; be x inches. It follows that the perimeter of triangle P Q R is 9 + 9 + x inches. Since it's given that the perimeter of triangle P Q R is 31 inches, it follows that 9 + 9 + x = 31 , or 18 + x = 31 . Subtracting 18 from both sides of this equation gives x = 13 . Therefore, the length, in inches, of Q R &macr; is 13 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Question points