Question

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 a triangle
$=\frac{1}{2}\text{(product of the sides)}\times \text{sine of the included angle)}$
$=\frac{1}{2}R\sin 2B\cdot \sin (180°-2A)$
$=\frac{1}{2}{R}^2\sin 2A\cdot \sin 2B\cdot \sin 2C$