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UPSC CDS 16 3 hindi Reviewed images Q8

ABC is a triangle right angled at C as shown in the figure below. Which one of the following is correct?

This question was previously asked in
CDS Maths Previous Paper 1 (Held On: 14 Feb 2016)
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  1. AQ2 + AB2 = BP2 + PQ2
  2. AQ2 + PQ2 = AB2 + BP2
  3. AQ2 + BP2 = AB2 + PQ2
  4. AQ2 + AP2 = BK2 + KQ2

Answer (Detailed Solution Below)

Option 3 : AQ2 + BP2 = AB2 + PQ2
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Detailed Solution

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Formula Used:

In a right-angled triangle ,WhatsAppImage20211226at94200PM-660x414

AC2 = AB2 + BC2 (Pythagoras theorem)

Calculation:

In triangle AQC

Using above theorem

AQ2 = AC2 + QC2                

Similarly

In triangle PBC

PB2 = PC2 + BC2

Adding both the equations

⇒ AQ2 + BP2 = (AC2 + BC2) + (PC2 + QC2)

In triangle ABC and PQC

⇒ AB2 = AC2 + BC2 and PQ2 = PC2 + QC2                    

Substituting back in the equation

⇒ AQ2 + BP2 = AB2 + PQ2

∴ Correct answer is option 3)

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