If a right angled triangle ABC of maximum `Delta` area is inscribed in a circle of radius R , then

Options

A. `Delta=2R^(2)`
B. `r=(sqrt2-1)R`
C. `1/(r_(1))+1/(r_(2))+1/(r_(3))=(sqrt2-1)/R`
D. `s=(sqrt2-1)R`

Explanation

To solve the problem, we need to find the maximum area of a right-angled triangle inscribed in a circle of radius \( R \).

### Step-by-Step Solution:

1. **Understanding the Right-Angled Triangle in a Circle**:
A right-angled triangle inscribed in a circle has its hypotenuse as the diameter of the circle. This is a consequence of Thales' theorem.

2. **Finding the Base and Height**:
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