Chords xy and PQ office circle intersect externally at the if xy is equals to 5 cm PQ = 3 cm and set q is equals to 4 cm the length of zy is

To solve the problem involving the chords \(XY\) and \(PQ\) intersecting externally, we can use the property of intersecting chords:

If two chords \(XY\) and \(PQ\) intersect outside the circle, the following relationship holds:

\[
XY \times YZ = PQ \times QZ
\]

Here, we know:
- \(XY = 5 \, \text{cm}\)
- \(PQ = 3 \, \text{cm}\)
- \(QZ = 4 \, \text{cm}\)

Let \(ZY = x\) (the length we want to find). Therefore, we can rewrite the relationship as:

\[
XY \times ZY = PQ \times QZ
\]

Substituting the known values:

\[
5 \times x = 3 \times 4
\]

Calculating the right side:

\[
5x = 12
\]

Now, solving for \(x\):

\[
x = \frac{12}{5} = 2.4 \, \text{cm}
\]

Thus, the length of \(ZY\) is \(2.4 \, \text{cm}\).

If you have any questions or need further details, feel free to ask! Here are some related questions for deeper exploration:

1. What are other properties of intersecting chords in circles?
2. How does the length of a chord relate to the radius of a circle?
3. Can you provide examples of similar problems with different values?
4. What is the formula for the area of a triangle formed by two chords in a circle?
5. How would the solution change if the intersection was internal instead of external?

**Tip:** Always sketch the problem when working with geometry, as it helps visualize relationships between different elements!

Chords XY and PQ in a circle intersect externally; if XY = 5 cm, PQ = 3 cm, and QZ = 4 cm, what is the length of ZY?

Explore the solution to find the length of ZY when chords XY and PQ intersect externally in a circle, with XY = 5 cm, PQ = 3 cm, and QZ = 4 cm. Learn the properties of intersecting chords and relevant geometry theorems. Ideal for Grades 7-9.

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