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Q.

Consider three lines as follows.L1:5x−y+4=0L2:3x−y+5=0L3:x+y+8=0If these lines enclose a triangle ABC and sum of the square of the tangent to the angles can be expressed in the form p/q, where p and Q are relatively prime numbers, then the value of p+q is

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a

500

b

450

c

230

d

465

answer is D.

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Detailed Solution

Arranging the lines in descending order of slope, we have m1=5, m2=3, and m3=−1∴ tanA=m1−m21+m1m2=21+15=18tanB=m2−m31+m2m3=3+11−3=−2tanC=m3−m11+m3m1=−1−51−5=32∑tan2A=164+4+94=1+256+14464=40164or p+q=465

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Consider three lines as follows.L1:5x−y+4=0L2:3x−y+5=0L3:x+y+8=0If these lines enclose a triangle ABC and sum of the square of the tangent to the angles can be expressed in the form p/q, where p and Q are relatively prime numbers, then the value of p+q is