Question

P and Q are two points on a circle of centre C and radius $\alpha$ the angle PCQ being $2\theta$ then the length of PQ is

• A. $2\alpha cos\left(\theta \right)$
• B. $2\alpha sin\left(\theta \right)$
  
• C. $2\alpha cos\left(2\theta \right)$
  
• D. $2\alpha sin\left(2\theta \right)$
  

Answer 1

The correct option is B $2\alpha sin\left(\theta \right)$

In $△PCQ$
By cosine rule: $\cos 2\theta =\frac{{\alpha }^2+{\alpha }^2-{PQ}^2}{2{\alpha }^2}$
$\Rightarrow PQ=\alpha \sqrt{2(1-\cos 2\theta )}=2\alpha \sin \theta$