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

Explanation:

Step1: Apply the chord - chord intersection theorem

When two chords $MN$ and $PQ$ intersect at a point $R$ inside a circle, the following relationship holds: $MR\times NR=PR\times QR$.
We know that $MR = 8$, $NR = 4$, and $PR = 5$. Substituting these values into the formula, we get $8\times4=5\times QR$.

Step2: Solve for $QR$

We have the equation $32 = 5\times QR$. Then $QR=\frac{32}{5}=6.4$.

Answer:

B. 6.4