Properties of Triangles 1 Question 9

9. In a PQR,R=π2, if tanP2 and tanQ2 are the roots of the equation ax2+bx+c=0(a0), then

(a) a+b=c

(b) b+c=a

(c) a+c=b

(d) b=c

(1999, 2M)

Show Answer

Answer:

Correct Answer: 9. (a)

Solution:

  1. It is given that, tan(P/2) and tan(Q/2) are the roots of the quadratic equation ax2+bx+c=0

 and R=π/2

tan(P/2)+tan(Q/2)=b/a

and tan(P/2)tan(Q/2)=c/a

Since, P+Q+R=180

P+Q=90

P+Q2=45tanP+Q2=tan45

tan(P/2)+tan(Q/2)1tan(P/2)tan(Q/2)=1b/a1c/a=1b/aaca=1bac=1b=aca+b=c



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