Circle And System Of Circles Question 309

Question: The angle between the tangents to the circle $ x^{2}+y^{2}=169 $ at the points (5, 12) and (12, -5), is

Options:

A) $ 30^{o} $

B) $ 45^{o} $

C) $ 60^{o} $

D) $ 90^{o} $

Show Answer

Answer:

Correct Answer: D

Solution:

The equations of tangents to the given circle will be $ 5x+12y=169 $ and $ 12x-5y=169 $ .

Obviously the angle between the tangents is $ 90^{o} $ .