Question

points q and r lie on a circle with center p. the radius of this circle is 9 inches. triangle pqr has a perimeter of 31 inches. what is the length, in inches, of qr? a) 13√2 b) 13 c) 9√2 d) 9

Explanation:

Step1: Recall circle - radius property

Since \(Q\) and \(R\) lie on a circle with center \(P\), \(PQ = PR=\text{radius} = 9\) inches.

Step2: Use perimeter formula

The perimeter of \(\triangle PQR\) is \(P = PQ+PR + QR\). We know \(P = 31\) inches, \(PQ = 9\) inches, and \(PR = 9\) inches. Substitute into the formula: \(31=9 + 9+QR\).

Step3: Solve for \(QR\)

First, simplify the right - hand side: \(9 + 9=18\). Then, we have the equation \(31=18 + QR\). Subtract 18 from both sides: \(QR=31 - 18=13\) inches.

Answer:

B. 13