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81. The measure of the angle between the internal and external bisectors of an angle is
  A.  90°
  B.  90°
  C.  90°
  D.  90°
     
   
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82. In a △ABC, ∠BAC = 90° and AB = 1/2BC. Then the measure of ∠ACB is:
  A.  60°
  B.  30°
  C.  45°
  D.  15°
     
   
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83. In a right angled △ABC, ∠ABC = 90°. BN is perpendicular to AC, AB = 8 cm, AC = 10 cm. Then AN : NC is
  A.  3 : 4
  B.  9 : 16
  C.  3 : 16
  D.  1 : 4
     
   
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84. ABC is a right angled triangle, right anggled at C and p is the length of the perpendicular from C on AB. If a, b and c are the length of the sides BC, CA and AB respectively, then
  A.  1/p2 = 1/b2 − 1/a2
  B.  1/p2 = 1/a2 + 1/b2
  C.  1/p2 + 1/a2 = − 1/b2
  D.  1/p2 = 1/a2 − 1/b2
     
   
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85. A point D is taken from the side of BC of a right-angled triangle ABC, where AB is a hypotenuse. Then
  A.  AB2 + CD2 = BC2 + AD2
  B.  CD2 + BD2 = 2AD2
  C.  AB2 + AC2 = 2AD2
  D.  AB2 = AD2 + BD2
     
   
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86. In △ ABC, ∠BAC = 90°, and D is the mid-point of BC. Then which of the following relations is true?
  A.  AD = BD = CD
  B.  AD = BD= 2CD
  C.  AD = 2BD = CD
  D.  2AD = BD = CD
     
   
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87. In △ ABC, ∠B is right angle. D is the mid-point of the side AC. If AB = 6 cm, BC = 8 cm, then the length of BD is:
  A.  4 cm
  B.  5 cm
  C.  8 cm
  D.  12 cm
     
   
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88. In △PQR, S and T are points on sides PR and PQ respectively such that ∠PQR = ∠PST. If PT = 5 cm, PS = 3 cm and TQ = 3 cm, then length of SR is
  A.  5 cm
  B.  6 cm
  C.  31/3 cm
  D.  41/3 cm
     
   
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89. In a △ ABC, D and E are two points on AB and AC respectively such that DE || BC, DE bisects the △ABC in two equal areas. Then the ratio DB : AB is
  A.  1 : √2
  B.  1 : 2
  C.  (√2 − 1) : √2
  D.  √2 : 1
     
   
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90. The perimeter of two similar triangels △ ABC and △ PQR are 60 cm and 36 cm respectively. If PQ = 18 cm, then AB is:
  A.  20 cm
  B.  24 cm
  C.  36 cm
  D.  30 cm
     
   
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