Length of two chords PQ and QR of a circle is 7 cm each and the radius of the circle is 7 cm then what is the length of PR

Given that the two chords \( PQ \) and \( QR \) each have a length of 7 cm, and the radius of the circle is also 7 cm, we need to find the length of chord \( PR \). 

Let’s approach this problem step by step:

### Step 1: Understanding the Geometry

The chords \( PQ \) and \( QR \) share the point \( Q \). Hence, \( PQR \) forms an isosceles triangle inscribed in the circle, with \( PQ = QR = 7 \, \text{cm} \). We also know that the center of the circle is equidistant from all points on the circumference, with a radius of 7 cm.

### Step 2: Applying the Geometry of Circles

Since the lengths of the chords are equal and the radius of the circle is the same as the length of the chords, \( PQR \) forms an equilateral triangle. This is because all sides of the triangle will be equal to the radius (7 cm), meaning that \( PR \), being the third side of the triangle, will also have a length of 7 cm.

### Conclusion:

The length of chord \( PR \) is \( 7 \, \text{cm} \).

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Would you like more details or have any further questions? Here are some additional questions to consider:

1. How do we prove the relationship between the chords and the radius mathematically?
2. What is the general formula for finding the length of a chord in a circle?
3. How does the angle subtended by equal chords relate to the central angle?
4. Can we apply Pythagoras' theorem to verify the result?
5. How would the result change if \( PQ \) and \( QR \) were not equal?

**Tip:** In problems involving circles, symmetry and geometric properties (such as angles or distances from the center) are often key to simplifying the solution.

Length of two chords PQ and QR of a circle is 7 cm each and the radius of the circle is 7 cm then what is the length of PR?

Learn how to find the length of chord PR in a circle where the two chords PQ and QR are each 7 cm long, and the radius is also 7 cm. This problem covers circle geometry, the properties of chords, and equilateral triangles, suitable for students in Grades 9-10.

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