Questions: Use the diagram to answer the question. MN and PQ are chords that intersect at point R. MR=8 NR=4 PR=5 *not drawn to scale What is QR ? A. 2.5 B. 6.4 C. 7 D. 9 E. 10

Use the diagram to answer the question.
MN and PQ are chords that intersect at point R.

MR=8
NR=4
PR=5
*not drawn to scale

What is QR ?
A. 2.5
B. 6.4
C. 7
D. 9
E. 10

Transcript text: Use the diagram to answer the question. $\overline{M N}$ and $\overline{P Q}$ are chords that intersect at point $R$. \[ \begin{array}{l} M R=8 \\ N R=4 \\ P R=5 \end{array} \] *not drawn to scale What is $Q R$ ? A. 2.5 B. 6.4 C. 7 D. 9 E. 10

Solution

Solution Steps

Step 1: Identify the given values

$ MR = 8 $
$ NR = 4 $
$ PR = 5 $

Step 2: Apply the intersecting chords theorem

The intersecting chords theorem states that if two chords intersect at a point, the products of the lengths of the segments of each chord are equal. Therefore: \[ MR \times NR = PR \times QR \]

Step 3: Substitute the given values into the equation

\[ 8 \times 4 = 5 \times QR \] \[ 32 = 5 \times QR \]

Step 4: Solve for $ QR $

\[ QR = \frac{32}{5} \] \[ QR = 6.4 \]