SSC Quantitative Aptitude Geometry Question Bank

done Triangles and Their Properties (I) Total Questions - 33

• question_answer1)
  In a triangle ABC, \[\angle A=70{}^\circ ,\]\[\angle B=80{}^\circ \]and D is the incentre of \[\Delta \,ABC.\] If \[\angle ACB=2x{}^\circ \]and \[\angle BDC=y{}^\circ .\]Then values of x and y, respectively are [SSC CGL Tier II, 2017]
  A)
  15,130 done clear
  B)
  15,125 done clear
  C)
  35, 40 done clear
  D)
  30,150 done clear
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• question_answer2)
  In a right angled triangle ADEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is [SSC CGL Tier II, 2017]
  A)
  3 cm done clear
  B)
  4 cm done clear
  C)
  6 cm done clear
  D)
  12 cm done clear
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• question_answer3)
  D and E are points on the sides AB and AC respectively of \[\Delta \,ABC.\]such that DE is parallel to BC and AD : DB =4.5, CD and BE intersect each other at F. Then, the ratio of the areas of \[\Delta DEF\]and\[\Delta CBF\] [SSC CGL Tier II, 2017]
  A)
  16 : 25 done clear
  B)
  16 : 81    done clear
  C)
  81 : 16 done clear
  D)
  4 : 9 done clear
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• question_answer4)
  If O is the orthocenter of a triangle ABC and \[\angle BOC=100{}^\circ ,\]the measure of \[\angle BAC\]is [SSC CGL Tier II, 2017]
  A)
  \[100{}^\circ \] done clear
  B)
  \[180{}^\circ \] done clear
  C)
  \[80{}^\circ \] done clear
  D)
  \[200{}^\circ \] done clear
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• question_answer5)
  \[\Delta \,ABC.\]is an isosceles right angled triangle having \[\angle C=90{}^\circ .\] If D is any point on AB, then \[A{{D}^{2}}+B{{D}^{2}}\]is equal to [SSC CGL Tier II, 2017]
  A)
  \[C{{D}^{2}}\] done clear
  B)
  \[2C{{D}^{2}}\] done clear
  C)
  \[3C{{D}^{2}}\] done clear
  D)
  \[4C{{D}^{2}}\] done clear
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• question_answer6)
  Given that the ratio of altitudes of two triangles is 4 : 5, ratio of their areas is 3 : 2. The ratio of their corresponding base is [SSC CGL Tier II, 2015]
  A)
  8 : 15 done clear
  B)
  15 : 8 done clear
  C)
  8 : 5 done clear
  D)
  5 : 8 done clear
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• question_answer7)
  In \[\Delta \,ABC,\]\[\angle \,BAC=90{}^\circ \] and \[AD\bot BC.\]if \[BD=3\,cm\]and \[CD=4\,cm,\]then the length (in cm) of AD is [SSC CGL Tier II, 2015]
  A)
  6 done clear
  B)
  \[2\sqrt{3}\] done clear
  C)
  5 done clear
  D)
  3.5 done clear
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• question_answer8)
  The centroid of a\[\Delta \,ABC\]is G. The area of \[\Delta \,ABC.\]is \[60\,c{{m}^{2}}.\]The area of GBC is [SSC CGL Tier II, 2015]
  A)
  \[40\text{ }c{{m}^{2}}\] done clear
  B)
  \[20\,\,c{{m}^{2}}\] done clear
  C)
  \[10\,\,c{{m}^{2}}\] done clear
  D)
  \[30\,\,c{{m}^{2}}\] done clear
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• question_answer9)
  In \[\Delta ABC,\] \[DE\parallel BC\]where D is a point on AB and E is a point on AC. DE divides the area of \[\Delta \,ABC\]into two equal parts. Then, DB: AB is equal to [SSC CGL Tier II, 2015]
  A)
  \[\sqrt{2}:(\sqrt{2}-1)\] done clear
  B)
  \[(\sqrt{2}+1):\sqrt{2}\] done clear
  C)
  \[(\sqrt{2}-1):\sqrt{2}\] done clear
  D)
  \[\sqrt{2}:(\sqrt{2}+1)\] done clear
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• question_answer10)
  If 0 is the circumcentre of a triangle ABC lying inside the triangle, then \[\angle OBC+\angle BAC\] is equal to                [SSC CGL Tier II, 2015]
  A)
  \[90{}^\circ \] done clear
  B)
  \[110{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
  \[-120{}^\circ \] done clear
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• question_answer11)
  AD is perpendicular to the internal bisector of \[\angle ABC\] of \[\Delta ABC.\] DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm) is [SSC CGL Tier II, 2015]
  A)
  8 done clear
  B)
  4 done clear
  C)
  3 done clear
  D)
  6 done clear
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• question_answer12)
  In a triangle ABC, \[\angle \,A+\frac{1}{2}\angle B+\angle \,C=140{}^\circ \] then \[\angle \,B\] is [SSC CGL Tier II, 2014]
  A)
  \[50{}^\circ \] done clear
  B)
  \[80{}^\circ \] done clear
  C)
  \[40{}^\circ \] done clear
  D)
  \[60{}^\circ \] done clear
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• question_answer13)
  G is the centroid of the equilateral \[\Delta \,ABC\] If AB = 10 cm, then length of AG is [SSC CGL Tier II,2014]
  A)
  \[\frac{5\sqrt{3}}{3}\,cm\] done clear
  B)
  \[\frac{10\sqrt{3}}{3}\,cm\] done clear
  C)
  \[5\sqrt{3}\] done clear
  D)
  \[10\sqrt{3}\] done clear
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• question_answer14)
  In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively If AB = 2AD, then DE : BC is [SSC CGL Tier II, 2014]
  A)
  2 : 3 done clear
  B)
  2 : 1 done clear
  C)
  1 : 2 done clear
  D)
  1 : 3 done clear
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• question_answer15)
  ABC is an isosceles triangle such that AB = AC and AD is the median to the base BC with \[\angle \,\,ABC=35{}^\circ .\]Then, \[\angle \,BAD\] is [SSC CGL Tier II, 2014]
  A)
  \[35{}^\circ \] done clear
  B)
  \[55{}^\circ \] done clear
  C)
  \[70{}^\circ ~\] done clear
  D)
  \[110{}^\circ \] done clear
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• question_answer16)
  \[\Delta \,ABC\]is an isosceles triangle and \[\overline{AB}=\overline{AC}=2a\] unit, \[\overline{BC}=a\] unit. Draw \[\overline{AD}\bot \overline{BC}\]and find the length of \[\overline{AD}.\]
  A)
  \[\sqrt{15}\,a\] unit done clear
  B)
  \[\frac{\sqrt{15}}{2}\,a\]unit done clear
  C)
  \[\sqrt{17}\,a\]unit done clear
  D)
  \[\frac{\sqrt{17}}{2}\,a\] unit done clear
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• question_answer17)
  A point D is taken from the side BC of a right angled \[\Delta ABC,\]where AB is hypotenuse. Then,
  A)
  \[A{{B}^{2}}+C{{D}^{2}}=B{{C}^{2}}+A{{D}^{2}}\] done clear
  B)
  \[C{{D}^{2}}+B{{D}^{2}}=2\,A{{D}^{2}}\] done clear
  C)
  \[A{{B}^{2}}+A{{C}^{2}}=2\,A{{D}^{2}}\] done clear
  D)
  \[A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\] done clear
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• question_answer18)
  In a right angled triangle, the product of two sides is equal to half of the square of the third side, i.e., hypotenuse. One of the acute angles must be
  A)
  \[60{}^\circ ~\] done clear
  B)
  \[30{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
  \[15{}^\circ \] done clear
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• question_answer19)
  If ABC is an equilateral triangle and D is a point on BC such that \[AD\bot BC,\] then
  A)
  AB : BD = 1 : 1 done clear
  B)
  AB : BD = 1 : 2 done clear
  C)
  AB : BD = 2 : 1 done clear
  D)
  AB : BD = 3 : 2 done clear
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• question_answer20)
  \[\angle \,A,\,\angle \,B\]and\[\angle \,C\]are three angles of a triangle. If \[\angle A-\angle B=15{}^\circ ,\]\[\angle B-\angle C=30{}^\circ \] then \[\angle A,\]\[\angle B\] and \[\angle \,C\]are
  A)
  \[80{}^\circ ,\]\[60{}^\circ ,\]\[40{}^\circ \] done clear
  B)
  \[70{}^\circ ,\]\[50{}^\circ ,\]\[60{}^\circ \] done clear
  C)
  \[80,\]\[65{}^\circ ,\]\[35{}^\circ \]         done clear
  D)
  \[80{}^\circ ,\]\[55{}^\circ ,\]\[45{}^\circ \] done clear
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• question_answer21)
  D and E are two points on the sides AC and BC respectively, of \[\Delta \,ABC\]such that DE = 18 cm, CE = 5 cm and\[\angle DEC=90{}^\circ .\]If \[\tan \,\angle ABC=3.6,\] AC : CD is equal to
  A)
  BC : 2 CE done clear
  B)
  2 CE : BC done clear
  C)
  2 BC : CE done clear
  D)
  CE : 2 BC done clear
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• question_answer22)
  If O is the orthocenter of the \[\Delta \,ABC\]and \[\angle BAC=80{}^\circ ,\] then measure of \[\angle BOC\]is
  A)
  \[80{}^\circ \] done clear
  B)
  \[100{}^\circ \] done clear
  C)
  \[120{}^\circ \] done clear
  D)
  \[90{}^\circ \] done clear
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• question_answer23)
  In \[\Delta ABC,\]\[DE\parallel BC,\]where DE intersects AB and AC at the points D and E respectively. If \[AD=6\,cm,\]cm,\[DB=12x-6\,cm,\]\[AE=2x\,cm\]and\[CE=16-2x\text{ }cm,\] then the value of x is
  A)
  6 cm done clear
  B)
  4 cm done clear
  C)
  2 cm done clear
  D)
  8 cm done clear
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• question_answer24)
  From the circumcentre I of the triangle ABC, perpendicular ID is drawn on BC. If \[\angle BAC=60{}^\circ ,\] then the value of \[\angle BID\] is
  A)
  \[75{}^\circ \] done clear
  B)
  \[60{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
  \[80{}^\circ \] done clear
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• question_answer25)
  In ABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR = 2 cm, then BC is equal to
  A)
  4 cm done clear
  B)
  2 cm done clear
  C)
  12 cm done clear
  D)
  6 cm done clear
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• question_answer26)
  The sides BC, CA and AB of \[\Delta ABC,\] have been produced to D, E and F respectively as shown in the figure, forming exterior angles \[\angle ACD,\]\[\angle BAD\]and\[\angle CBF\] Then,\[\angle ACD+\angle BAE+\angle CBF\] is equal to
  A)
  \[240{}^\circ \] done clear
  B)
  \[300{}^\circ \] done clear
  C)
  \[320{}^\circ \] done clear
  D)
  \[360{}^\circ \] done clear
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• question_answer27)
  ABC is a right angled triangle such that \[AB=a-b,\]\[BC=a\] and \[CA=a+b.\]D is a point on BC such that BD = AB. The ratio of BD : DC for any value of a and b is given by
  A)
  3 : 2 done clear
  B)
  4 : 3 done clear
  C)
  5 : 4 done clear
  D)
  3 : 1 done clear
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• question_answer28)
  ABC is a triangle, where\[BC=2AB,\]\[\angle B=\text{ }30{}^\circ \]and \[\angle A=90{}^\circ .\]The magnitude of the side AC is
  A)
  \[\frac{2BC}{3}\] done clear
  B)
  \[\frac{3BC}{4}\] done clear
  C)
  \[\frac{BC}{\sqrt{3}}\] done clear
  D)
  \[\frac{\sqrt{3}BC}{2}\] done clear
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• question_answer29)
  The bisectors BI and CI of \[\angle B\]and \[\angle C\]of a \[\Delta ABC\]meet in I. What is \[\angle BIC\]?
  A)
  \[90{}^\circ -\frac{A}{A}\] done clear
  B)
  \[90{}^\circ +\frac{A}{A}\] done clear
  C)
  \[90{}^\circ -\frac{A}{2}\] done clear
  D)
  \[90{}^\circ +\frac{A}{2}\] done clear
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• question_answer30)
  ABC is a triangle right angled at A and a perpendicular AD is drawn on the hypotenuse BC. Whatis.BC.AD?
  A)
  \[AB\cdot AC\] done clear
  B)
  \[AB\cdot AD\] done clear
  C)
  \[CA\cdot CD\] done clear
  D)
  \[AD\cdot DB\] done clear
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• question_answer31)
  If AD is the internal angle bisector of \[\Delta ABC\] with AB = 3 cm and AC = 1 cm, then what is BD : BC?
  A)
  1 : 3 done clear
  B)
  1 : 4 done clear
  C)
  2 : 3 done clear
  D)
  3 : 4 done clear
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• question_answer32)
  In a \[\Delta ABC,\] \[\angle BCA=60{}^\circ \] and \[A{{B}^{2}}=B{{C}^{2}}+C{{A}^{2}}+X.\] What is the value X?
  A)
  \[(BC)(CA)\] done clear
  B)
  \[-\left( BC \right)\,\,\left( AC \right)\] done clear
  C)
  \[(AB)(BC)\] done clear
  D)
  Zero done clear
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• question_answer33)
  In a \[\Delta ABC,\] XY is drawn parallel to BC, cutting sides at X and Y, where AB = 4.8 cm, BC = 7.2 cm and BX = 2 cm. What is the length of XY?
  A)
  4 cm done clear
  B)
  4.1 cm done clear
  C)
  4.2 cm done clear
  D)
  4.3 cm done clear
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