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question_answer1) In \[\Delta ABC\] if \[\frac{{{r}_{1}}}{\left( s-b \right)\left( s-c \right)}+\frac{{{r}_{2}}}{\left( s-c \right)\left( s-a \right)}+\frac{{{r}_{3}}}{\left( s-a \right)\left( s-b \right)}=\frac{k}{r},\] Then find value of k.
question_answer2) The sides of a triangle are \[3+\sqrt{3},\,\,2\sqrt{3}\] and \[\sqrt{6}.\] if the least angle is \[k{}^\circ \] then find k.
question_answer3) In \[\Delta ABC\], if \[a=3,\text{ }b=4,\text{ }c=5,\] then sin 2B is equal to \[\frac{24}{k},\] then find k.
question_answer4) Ratio of sides in a triangle are \[3:7:8.\] if circumradius (R): inradius \[\left( r \right)=k:2\] then find k.
question_answer5) Find the radius of the incircle of a triangle whose sides are 18, 24 and 30.
question_answer6) In a \[\Delta ABC\], if \[b+c=3a,\] then find the value of \[\cot \frac{B}{2}\cot \frac{C}{2}.\]
question_answer7) In a \[\Delta ABC\], \[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\] and the side \[a\text{ }=\text{ }2,\] then find area of the triangle.
question_answer8) In a \[\Delta ABC\] if \[a=3,b=4,c=5\] then find its circumradius.
question_answer9) In an equilateral triangle of each side \[2\sqrt{3}cm\], then find radius of the circum circle.
question_answer10) If the area of a triangle is 81 and its perimeter is 27 then find its inradius.
question_answer11) In\[\Delta ABC\], if \[{{a}^{2}}+{{b}^{2}}=671{{c}^{2}}\]then find \[\frac{\cot C}{\cot A+\cot B}.\]
question_answer12) In a \[\Delta ABC\], \[a=6,\,\,b=3\] and cos\[C=\frac{\sqrt{3}}{2},\] then find area of triangle.
question_answer13) In \[\Delta ABC\], if \[a=3,\text{ }b=5,\text{ }c=4,\] then find value of \[\sin \frac{B}{2}+\cos \frac{B}{2}.\]
question_answer14) In any\[\Delta ABC\], find value of \[\left( \frac{b-c}{a} \right){{\cos }^{2}}\left( \frac{A}{2} \right)\]\[+\left( \frac{c-a}{b} \right){{\cos }^{2}}\left( \frac{B}{2} \right)+\left( \frac{a-b}{2} \right){{\cos }^{2}}\left( \frac{C}{2} \right).\]
question_answer15) In a\[\Delta ABC\], if\[\left( b+c-a \right)\tan \,\left( \frac{A}{2} \right)\]is equal to \[\frac{k\Delta }{s}\] then find k.
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