I have got $3$ points say $(x_1,y_1)$, $(x_2,y_2)$ and the point of intersection $(x,y)$. I need to know the angle of convex angle of intersection of points. I need to whether the angle of intersection is acute or obtuse. The lines can be of any orientation. I need this to find which angle bisector I should choose.
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Find both bisectors. The one to which the perpendicular distance from the points is smaller is acute angle bisector. – L__ Mar 13 '14 at 06:55
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Yes, I can do that but in my case if the angle is obtuse i need to choose acute bisector and viz. For that i need to know the angle whether is acute or obtuse. – Raajesh Kotteeswaran Mar 13 '14 at 07:03
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Hint: It is the angle between the vectors $$u=(x-x_1,y-y_1),\ \ v=(x-x_2,y-y_2)$$ It is $$\cos\theta=\frac{u\cdot v}{||u||.||v||}$$
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The slope of the bisectors of the angle between two lines with slope $m_1,m_2$ is $$m=\frac{a}{b+\sqrt{a^2+b^2}}\ \ \text{and}\ \ m=\frac{a}{b-\sqrt{a^2+b^2}}$$ where $a=m_1+m_2$ and $b=1-m_1m_2$
Semsem
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Hi Semsem, thanks for the hint which worked. If the dot product is -ve the angle is obtuse else it is acute. – Raajesh Kotteeswaran Mar 13 '14 at 09:26
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Yes, @Semsem now I have one more query is it possible to find the slope of the angle bisector for the angle we found. Because using tangent slope method involving slopes of the lines (m1 and m2) it gives me the opposite bisectors at times (i.e) if i calculate for obtuse it gives me acute angle bisectors at times. Is there a way to find the exact bisector for the angle found. Thanks – Raajesh Kotteeswaran Mar 14 '14 at 01:50
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Hi @semsem, I have marked it to answer but i cant upvote due to reputation constraint. Thanks a lot – Raajesh Kotteeswaran Mar 14 '14 at 07:36
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Use the fact that locus of distance from two lines is same is angle bisector.
Acute angle bisector : if $2\theta<\frac{\pi}2$ then $\tan\theta<1$
$\theta$ is angle between bisector and one of the lines.
Angle between 2 lines :
evil999man
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