JEE Main & Advanced Mathematics Trigonometric Equations Question Bank

done Circle connected with triangle Total Questions - 22

• question_answer1)
  In \[\Delta ABC,\ \,2{{R}^{2}}\sin A\sin B\sin C=\]
  A)
  \[{{s}^{2}}\] done clear
  B)
  \[ab+bc+ca\] done clear
  C)
  \[\Delta \] done clear
  D)
  None of these done clear
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• question_answer2)
  In \[\Delta ABC,\]if \[b=6,\,c=8\,\]and \[\angle A=90{}^\circ \], then R=
  A)
  3 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  7 done clear
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• question_answer3)
  If the sides of a triangle are in ratio 3 : 7 : 8, then R : r is equal to  
  A)
  2 : 7 done clear
  B)
  7 : 2 done clear
  C)
  3 : 7 done clear
  D)
  7 : 3 done clear
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• question_answer4)
  If the sides of triangle are 13, 14, 15, then the radius of its incircle is [EAMCET 1987]
  A)
  \[\frac{67}{8}\] done clear
  B)
  \[\frac{65}{4}\] done clear
  C)
  4 done clear
  D)
  24 done clear
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• question_answer5)
  The inradius of the triangle whose sides are 3, 5, 6, is  [EAMCET 1982]
  A)
  \[\sqrt{8/7}\] done clear
  B)
  \[\sqrt{8}\] done clear
  C)
  \[\sqrt{7}\] done clear
  D)
  \[\sqrt{7/8}\] done clear
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• question_answer6)
  In an equilateral triangle of side \[2\sqrt{3}\]cm, the circum-radius is [EAMCET 1978]
  A)
  1 cm done clear
  B)
  \[\sqrt{3}\]cm done clear
  C)
  2 cm done clear
  D)
  \[2\sqrt{3}\]cm done clear
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• question_answer7)
  In an equilateral triangle the inradius and the circum-radius are connected by [EAMCET 1983]
  A)
  \[r=4R\] done clear
  B)
  \[r=R/2\] done clear
  C)
  \[r=R/3\] done clear
  D)
  None of these done clear
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• question_answer8)
  In any triangle ABC, \[a\cot A+b\cot B+c\cot C=\]
  A)
  \[r+R\] done clear
  B)
  \[r-R\] done clear
  C)
  \[2(r+R)\] done clear
  D)
  \[2(r-R)\] done clear
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• question_answer9)
  If the radius of the circumcircle of an isosceles triangle \[PQR\] is equal to \[PQ(=PR),\]then the angle P is [IIT Screening 1992; Pb. CET 2004]
  A)
  \[\frac{\pi }{6}\] done clear
  B)
  \[\frac{\pi }{3}\] done clear
  C)
  \[\frac{\pi }{2}\] done clear
  D)
  \[\frac{2\pi }{3}\] done clear
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• question_answer10)
  In a triangle ABC, \[a:b:c=4:5:6\]. The ratio of the radius of the circumcircle to that of the incircle is [IIT 1996]
  A)
  \[\frac{16}{9}\] done clear
  B)
  \[\frac{16}{7}\] done clear
  C)
  \[\frac{11}{7}\] done clear
  D)
  \[\frac{7}{16}\] done clear
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• question_answer11)
  Which is true in the following [UPSEAT 1999]
  A)
  \[a\cos A+b\cos B+c\cos C=R\sin A\sin B\sin C\] done clear
  B)
  \[a\cos A+b\cos B+c\cos C=2R\sin A\sin B\sin C\] done clear
  C)
  \[a\cos A+b\cos B+c\cos C=4R\sin A\sin B\sin C\] done clear
  D)
  \[a\cos A+b\cos B+c\cos C=8R\sin A\sin B\sin C\] done clear
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• question_answer12)
  If \[x,\,y,\,z\]are perpendicular drawn \[a,\,b\] and \[c\], then the value of  \[\frac{bx}{c}+\frac{cy}{a}+\frac{az}{b}\]will be [UPSEAT 1999]
  A)
  \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{2R}\] done clear
  B)
  \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{R}\] done clear
  C)
  \[\frac{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}{4R}\] done clear
  D)
  \[\frac{2({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}{R}\] done clear
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• question_answer13)
  If the length of the sides of a triangle are 3, 4 and 5 units, then R (the circumradius) is [UPSEAT 2000]
  A)
  2.0 unit done clear
  B)
  2.5 unit done clear
  C)
  3.0 unit done clear
  D)
  3.5 unit done clear
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• question_answer14)
  If R is the radius of the circumcircle of the \[\Delta ABC\]and \[\Delta \]is its area, then [Karnataka CET 2000]
  A)
  \[R=\frac{a+b+c}{\Delta }\] done clear
  B)
  \[R=\frac{a+b+c}{4\Delta }\] done clear
  C)
  \[R=\frac{abc}{4\Delta }\] done clear
  D)
  \[R=\frac{abc}{\Delta }\] done clear
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• question_answer15)
  The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is [AIEEE 2003]
  A)
  \[a\cot \left( \frac{\pi }{n} \right)\] done clear
  B)
  \[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\] done clear
  C)
  \[a\cot \left( \frac{\pi }{2n} \right)\] done clear
  D)
  \[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\] done clear
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• question_answer16)
  In a \[\Delta ABC,\ {{r}_{1}}<{{r}_{2}}<{{r}_{3}},\]then [EAMCET 2003]
  A)
  \[a<b<c\] done clear
  B)
  \[a>b>c\] done clear
  C)
  \[b<a<c\] done clear
  D)
  \[a<c<b\] done clear
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• question_answer17)
  The radius of the in circle of triangle when sides are 18, 24 and 30 cms is [Pb. CET 2004]
  A)
  2 cm done clear
  B)
  4 cm done clear
  C)
  6 cm done clear
  D)
  9 cm done clear
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• question_answer18)
  If the sides of the triangle are \[5K,\ 6K,\ 5K\]and radius of incircle is 6 then value of K is equal to [Pb. CET 2004]
  A)
  4 done clear
  B)
  5 done clear
  C)
  6 done clear
  D)
  7 done clear
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• question_answer19)
  \[\frac{a\cos A+b\cos B+c\cos C}{a+b+c}=\] [Orissa JEE 2004]
  A)
  1/r done clear
  B)
  r/R done clear
  C)
  R/r done clear
  D)
  1/R done clear
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• question_answer20)
  In a triangle\[ABC\], if \[b=2,\,B=30{}^\circ \]then the area of circumcircle of triangle ABC in square units is  [Karnataka CET 2004]
  A)
  \[\pi \] done clear
  B)
  \[2\pi \] done clear
  C)
  \[4\pi \] done clear
  D)
  \[6\pi \] done clear
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• question_answer21)
  The circum-radius of the triangle whose sides are 13, 12 and 5 is [Karnataka CET 2005]
  A)
  15 done clear
  B)
  13/2 done clear
  C)
  15/2 done clear
  D)
  6 done clear
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• question_answer22)
  The area  of the equilateral triangle which containing three coins of unity radius is [IIT Screening 2005]
  A)
  \[6+4\sqrt{3}\ sq.\ units\] done clear
  B)
   \[8+\sqrt{3}\] sq. units done clear
  C)
  \[4+\frac{7\sqrt{3}}{2}\] sq. units done clear
  D)
  \[12+2\sqrt{3}\]sq. units done clear
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