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Question

In ABC, tanAand tanB are the roots ofpq(x2+1)=r2x. ThenABC is


A

A right-angled triangle

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B

Acute-angled triangle

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C

An obtuse-angled triangle

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D

An equilateral triangle

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Solution

The correct option is A

A right-angled triangle


Explanation For The Correct Option:

Determining ABC:

The given equation is

pq(x2+1)=r2x

This equation can be written as

pqx2-r2x+pq=0

This is a quadratic equation then

Sum of roots of this equation is =--r2pq

As given tanAand tanB are the roots of this equation

tanA+tanB=r2pq1Weknowthattan(A+B)=tanA+tanB1tanAtanBSubstitutingfromequation(1)tan(A+B)=r2pq1-1;tanAtanB=1=tan(A+B)=tan90°A+B=90°A+B+C=180°C=90°

As one of the angle in a triangle is right angled then it is a right-angled triangle.

Hence, the correct answer is option (A).


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