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A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
[JEE 2008, 4]
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?
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A straight line through the vertex P of a triangle PQR intersects the ...
Ans.

Option (d)

Let us suppose that a straight line through the vertex P of a given ?PQR intersects the side QR at the point S and the circum circle of the triangle PQR at the point T.

Now, the points P, Q, R and T are concyclic and hence PS.ST = QS.SR

Now we know that A.M > G.M

So, we have, (PS + ST)/ 2 > √PS.ST

1/ PS + 1/ ST > 2/ √PS.ST = 2/ √QS.SR

Also, (SQ + QR)/ 2 > √QS.SR

So, QR/2 > √QS.SR

1/√QS.SR > 2/QR

Hence, 2/ √QS.SR > 4/ QR

So, we obtain 1/ PS + 1/ ST > 2/ √QS.SR > 4/ QR.
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A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then[JEE 2008, 4]a)b)c)d)Correct answer is option 'D'. Can you explain this answer?
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A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then[JEE 2008, 4]a)b)c)d)Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then[JEE 2008, 4]a)b)c)d)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then[JEE 2008, 4]a)b)c)d)Correct answer is option 'D'. Can you explain this answer?.
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