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  • Ex: The angle between the two tangents from the origin to the circle (x − 7)2 + (y + 1)2 = 25 is 
    A) 0    
    B) π/3
    C) π/6                       
    D) π/2
    Correct answer: D
    Explanation & Trick:
    Any line through (0, 0) be y − mx = 0 and it is a tangent to circle (x−7)2 + (y+1)2 = 25, if 
     − 1 − 7m / √1+m2 =5 ⇒ m = 3 / 4, −4 / 3
    Therefore, the product of both the slopes is -1.                   
     i.e., 3 / 4 × − 4 / 3 = −1.
    Hence the angle between the two tangents is π / 2.  
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