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Points Q and R lie on a circle with center P. The radius of this circle is 9 inches. Triangle PQRhas a perimeter of 31 inches. What is the length, in inches, of QR? 13 2
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
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 PQ and RP of triangle PQR each have a length of 9 inches. Let the length of QR be x inches. It + + follows that the perimeter of triangle PQR is 9 9 x inches. Since it’s given that 31 9+9+ =31 the perimeter of triangle PQR is inches, it follows that x , or 18+ =31 18 =13 x . Subtracting from both sides of this equation gives x . 13 Therefore, the length, in inches, of QR is . 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.
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