In `DeltaDEF, /_EFD = 90^@, DF = 7 cm and EF = 24`. What is the ra dius (in cm) of the circum-circle of `DeltaDEF`?

Options

A. `26 `
B. `12.5 `
C. `13 `
D. `25 `

Answer

To find the radius of the circumcircle of triangle DEF, where angle EFD is 90 degrees, DF = 7 cm, and EF = 24 cm, we can follow these steps:

### Step 1: Identify the sides of the triangle
In triangle DEF, we have:
- DF = 7 cm (one leg)
- EF = 24 cm (the other leg)
- EFD = 90 degrees (right angle)

### Step 2: Use the Pythagorean theorem to find the hypotenuse
According to the Pythagorean theorem, the hypotenuse (DE) can be calculated using the formula:
\[ DE = \sqrt{DF^2 + EF^2} \]

Substituting the values:
\[ DE = \sqrt{7^2 + 24^2} \]
\[ = \sqrt{49 + 576} \]
\[ = \sqrt{625} \]
\[ = 25 \text{ cm} \]

### Step 3: Calculate the radius of the circumcircle
For a right triangle, the radius (R) of the circumcircle is half the length of the hypotenuse:
\[ R = \frac{DE}{2} \]
Substituting the value of DE:
\[ R = \frac{25}{2} \]
\[ = 12.5 \text{ cm} \]

### Final Answer
The radius of the circumcircle of triangle DEF is **12.5 cm**.

---