QJEEAdv08Maa36b: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Maa36b Solution: A straight line through the vertex p of a triangle PQR…

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QJEEAdv08Maa36b: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Maa36b Solution: A straight line through the vertex p of a triangle PQR…

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 :

Multiple Choice Options

A 1PS+1ST<2QS×SR
B 1PS+1ST>2QS×SR
C 1PS+1ST<4QR
D 1PS+1ST>4QR

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Accepted Answer

As S is not the centre of the circumcircle, there for PS $\neq$ ST and QS $\neq$ SR

IIT-JEE 2008 Paper 1 Offline Mathematics - Straight Lines and Pair of Straight Lines Question 82 English Explanation

Also, (PS)(ST) = (QS)(SR)

[ $∴$ from the properties of two intersecting chords in a circle]

$\Rightarrow$ A.M $\geq$ G.M

We get $\frac{\frac{1}{P S} + \frac{1}{S T}}{2} \geq \sqrt{\frac{1}{P S} \times \frac{1}{S T}}$

or

$\frac{1}{P S} + \frac{1}{S T} \geq \frac{2}{\sqrt{Q S \times S R}}$

$\frac{Q S + S R}{2} \geq \sqrt{Q S \times S R}$ ..... (i)

$\frac{1}{\sqrt{Q S \times S R}} \geq \frac{2}{Q R}$ .... (ii)

$\Rightarrow \frac{1}{P S} + \frac{1}{S T} \geq \frac{4}{Q R}$ From (i) and (ii)

QJEEAdv08Maa36b: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Maa36b Solution: A straight line through the vertex p of a triangle PQR…

Multiple Choice Options

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