IIT JEE , AIEEE Forum - Mathematics , Trignometry - Radon challenger series Part-3

Radon222

Match the column:

$\begin{tabular}{||c||l||l||} \hline S. no. & $Column 1$ & $Column 2$ \\ \\ \hline (A) & In a \bigtriangleup \text{ABC}, \text{if } 2a^2+b^2+c^2=2ac+2ab,then &(P) \bigtriangleupABC \text{is equilateral} \\ \\ \\ (B) & In a \bigtriangleup ABC , \text{if} a^2+b^2+c^2=\sqrt{2}b(c+a),then &(Q)\bigtriangleupABC \text{is rightangled} \\ \\ \\ (C) & In a \bigtriangleup ABC , \text{if} a^2+b^2+c^2=bc+ca\sqrt{3}&(R) \bigtriangleup ABC \text{is scalene}\\ \\ \\ & &(S)\bigtriangleup ABC \text{is rightangled+scalene}\\ \\ \\ & & (T)\text{Angles B,C,A are in AP} \\ \hline \end{tabular}$

Radon222

Actually I wanted to give a tougher one but the latex editor was not allowing the code

nadeemoidu

A )
By using AM-GM inequality on a² and b² we get
a² + b² >= 2ab

Equality holds when a=b

similarly a=c .

It is equilateral .

B and C)
c² = a² + b² - 2abcosC
and similarly for a² and b²

add the 3 equations and we get
a² + b² + c² = 2ab cosC + 2bc cosA + 2ac cosB

compare the coefficients of ab , bc and ca to find the angles.

LAMPARD

1)P,T
2)Q
3)

Radon222

Both the answers are wrong

akhil_o

A) P,T
B) Q,R,S
C) T

Radon222

Wrong !

elastiboysai

P T

Q

Q S R

Radon222

Wrong !

sivaramakh

pt
q
sr

Radon222

Elastiboysai has won challenger series Part-3 .If he likes then he can post his solution also for benefit of others.

amitp91

A-P
B-Q
C-R

elastiboysai

K the solutions

This method's fine if RHS is only a poss.

Radon222

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