Question

Q 2. In the following figure, the area of the pedal triangle is -

• A. $\frac{1}{2}{R}^2.\text{sin A.sin B.sin C}$
• B. $\frac{1}{2}{R}^2.\text{sin 2A.sin 2B.sin 2C}$
• C. $\frac{1}{2}{R}^2.\text{cos A.cos B.cos C}$
• D. None of these

Answer 1

The correct option is B $\frac{1}{2}{R}^2.\text{sin 2A.sin 2B.sin 2C}$

Since, area of $△=\frac{1}{2}$ (product of the sides) $\times$ (sine of the included angle)
$=\frac{1}{2}$ (R sin 2B) .sin(180° - 2A)
$=\frac{1}{2}{R}^2$.sin 2A.sin 2B.sin 2C