question_answer

The length \[{{60}^{o}}\]of a tangent, drawn from a point A to a circle is \[{{120}^{o}}\]of the radius r. The shortest distance from A to the circle is

A)  \[{{180}^{o}}\]                              

B) r

C)  \[\angle R={{138}^{o}}\]          

D)  \[\angle PQS\]

Correct Answer: C

Solution :

Join AO. Let AO intersects the circle at X. Since, \[\Rightarrow \]. [Radius is perpendicular to the tangent at point of contact.]             \[{{90}^{o}}\] \[\square ABCD\]             \[\Rightarrow \] \[\angle 1=\angle 2=\angle 3=\angle 4={{90}^{o}}\]             \[AB=CD\] \[AB||DC\]\[AD=BC\] \[AD||BC\]