Question

Given two circles intersecting orthogonally having length of common chord $\frac{24}{5}$ units radius of one of the circles is $3$ units then length of direct common tangent is

• A. $12$
• B. $3$
• C. $2\sqrt{6}$
• D. $6$

Answer 1

The correct option is C $2\sqrt{6}$

Let $\angle OAB=\angle A{O}^{\prime }B=\theta ⟹\sin \theta =\frac{\frac{12}{5}}{3}=\frac{4}{5}⟹r=4$

$d^2=O{O}^{\prime 2}-(r-3{)}^2=25-1=24⟹d=2\sqrt{6}$