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Maths-

General

Easy

Question

If in a triangle $comma blank open parentheses 1 minus fraction numerator r subscript 1 end subscript over denominator r subscript 2 end subscript end fraction close parentheses open parentheses 1 minus fraction numerator r subscript 1 end subscript over denominator r subscript 3 end subscript end fraction close parentheses equals 2 comma blank$ then the triangle is

Right angled
Isosceles
Equilateral
None of these

The correct answer is: Right angled

We have $open parentheses 1 minus fraction numerator s minus b over denominator s minus a end fraction close parentheses open parentheses 1 minus fraction numerator s minus c over denominator s minus a end fraction close parentheses equals 2$
$rightwards double arrow 2 open parentheses b minus a close parentheses open parentheses c minus a close parentheses equals 4 open parentheses s minus a close parentheses to the power of 2 end exponent$
$rightwards double arrow 2 open parentheses b c minus a c minus a b plus a to the power of 2 end exponent close parentheses equals open parentheses 2 s minus 2 a close parentheses to the power of 2 end exponent$
$rightwards double arrow 2 open parentheses b c minus a c minus a b plus a to the power of 2 end exponent close parentheses equals open parentheses b plus c minus a close parentheses to the power of 2 end exponent$
$rightwards double arrow a to the power of 2 end exponent equals b to the power of 2 end exponent plus c to the power of 2 end exponent$
Hence, triangle is right angled

Related Questions to study

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Which of the following is correct?

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