To solve the problem, we will use the information in the diagram. The goal is to find the length of the chord $PQ$ correct to 2 significant figures.

Key Information:

1. $OP = 14 \, \text{cm}$ (radius of the circle).
2. $OD = 8 \, \text{cm}$ (distance from the center $O$ to the midpoint of $PQ$).
3. $D$ is the midpoint of $PQ$, so $PD = DQ$.

Steps to Solve:

1. Right Triangle in Circle Geometry:

   • Triangle $ODP$ is a right triangle since $OD$ is perpendicular to the chord $PQ$ and passes through its midpoint.
   • Using Pythagoras' theorem: $OP^2 = OD^2 + PD^2$ Substituting values: $14^2 = 8^2 + PD^2$

2. Solve for $PD$: $196 = 64 + PD^2$ $PD^2 = 196 - 64 = 132$ $PD = \sqrt{132} \approx 11.49 \, \text{cm}$

3. Find $PQ$: Since $D$ is the midpoint of $PQ$: $PQ = 2 \times PD$ $PQ = 2 \times 11.49 \approx 22.98 \, \text{cm}$

Final Answer:

The length of the chord $PQ$ is approximately: $PQ = 23 \, \text{cm} \quad (\text{to 2 significant figures}).$

Would you like further clarification or additional steps explained? 😊

Related Questions:

1. What is the significance of the perpendicular distance $OD$ from the center to the chord?
2. How does Pythagoras' theorem apply to this scenario in circle geometry?
3. Can you determine the length of $PQ$ if $OD$ changes to 10 cm?
4. What is the formula for finding the length of a chord in a circle?
5. How does the radius affect the length of the chord for a fixed distance $OD$?

Tip:

In circle problems, the perpendicular from the center to the chord always bisects the chord.