Straight Line Question 395

Question: The triangle PQR is inscribed in the circle $ x^{2}+y^{2}=25 $ . If Q and R have co-ordinates (3,4) and (? 4, 3) respectively, then $ \angle QPR $ is equal to [IIT Screening 2000]

Options:

A) $ \frac{\pi }{2} $

B) $ \frac{\pi }{3} $

C) $ \frac{\pi }{4} $

D) $ \frac{\pi }{6} $

Show Answer

Answer:

Correct Answer: C

Solution:

  • Here the centre $ 0(0,0) $ . So ?m? of OQ is $ \frac{4}{3} $ and ?m? of OR is $ \frac{-3}{4} $ , \ $ \angle QOR=\frac{\pi }{2} $ Hence $ \angle QPR=\frac{1}{2}\times \frac{\pi }{2}=\frac{\pi }{4} $ .