In a `DeltaPQR,angle RPQ=90^(@),bar(PR)=6cmandbar(PQ)=8cm`, then the radius of the circumcircle of `DeltaPRR` is.
एक `DeltaPQR` में, `angle RPQ=90^(@),bar(PR)=6` सेमी और `bar(PQ)` = 8 सेमी., तो `anglePQR` के परिवृत्त की त्रिज्या कितनी होगी?

Options

A. 5 सेमी.
B. 3 सेमी.
C. 4 सेमी.
D. 4.5 सेमी.

Explanation

To find the radius of the circumcircle of triangle PQR, where angle RPQ is 90 degrees, we can follow these steps:

### Step 1: Identify the triangle and its sides
In triangle PQR, we know:
- Angle RPQ = 90 degrees
- PR = 6 cm
- PQ = 8 cm

### Step 2: Use the Pythagorean theorem to find the third side QR
Since triangle PQR is a right triangle, we can use the Pythagorean theorem, which states:
\[ QR^2 = PQ^2 + PR^2 \]

Substituting the known values:
\[ QR^2 = 8^2 + 6^2 \]
\[ QR^2 = 64 + 36 \]
\[ QR^2 = 100 \]

Now, taking the square root to find QR:
\[ QR = \sqrt{100} = 10 \text{ cm} \]

### Step 3: Calculate the circumradius (R) of triangle PQR
For a right triangle, the circumradius (R) can be calculated using the formula:
\[ R = \frac{C}{2} \]
where C is the length of the hypotenuse. In triangle PQR, QR is the hypotenuse.

So, substituting the value of QR:
\[ R = \frac{10}{2} = 5 \text{ cm} \]

### Conclusion
The radius of the circumcircle of triangle PQR is **5 cm**.

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