In triangle PQR, PS bisects angle QPR and QPS=60. With PQ=r, PR=q and QR=p as shown, the length PS is

GATE 2015 EE (EE2) – Question 7

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

In triangle PQR, PS bisects angle QPR and $\angle QPS=60^\circ$. With PQ=r, PR=q and QR=p as shown, the length PS is

Diagram for GATE 2015 EE (EE2) question 7

$(q+r)/(qr)$
$qr/(q+r)$
$\sqrt{q^2+r^2}$
$(q+r)^2/(qr)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $qr/(q+r)$

Explanation

The angle at P is twice 60°, namely 120°. The internal-angle-bisector length for adjacent sides q,r and included angle P is $PS=2qr\cos(P/2)/(q+r)$.

Substitute cos60°=1/2 to get **PS=qr/(q+r), B**. The formula follows by the angle-bisector theorem combined with the cosine rule, and has the correct dimension of length.

More Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation questions

GATE 2015 EE (EE2) Q8 – For distinct integers p,q,r,s define f as their maximum and g as their minimum. Define h…
GATE 2015 EE (EE2) Q9 – P,R,S,T,U form an arithmetic sequence. Which also do? I: 2P,2R,2S,2T,2U. II:…
GATE 2015 EE (EE2) Q10 – Branches M,N,O,P have these positions: M is 4 km north of N; P is 2 km south of O; N is 1…
GATE 2020 AE Q10 – The figure shows school P and Q enrolments during 2014–2018. Find the ratio of average…
GATE 2020 BT Q8 – Delhi and Agra are 233 km apart. P travels from Delhi to Agra; Q starts from Agra to Delhi…
GATE 2020 BT Q10 – The chart shows profit percentages of companies P and Q during 2013–2018. Both invest a…

All Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation questions →