Question

1. in the figures below, circle ( j cong ) circle ( k ) and arc ( mn cong ) arc ( pq ). determine ( pq ).

Explanation:

Step1: Set up the equation

Since Circle \( J \cong \) Circle \( K \) and arc \( MN \cong \) arc \( PQ \), their corresponding chord lengths are equal. So we set \( 2x + 1 = 3x - 7 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 1 = x - 7 \). Then add 7 to both sides: \( x = 8 \).

Step3: Find \( PQ \)

Substitute \( x = 8 \) into the expression for \( PQ \), which is \( 3x - 7 \). So \( 3(8) - 7 = 24 - 7 = 17 \).

Answer:

\( 17 \)