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31. ABC is an isosceles triangle with AB= AC. A circle through B touching AC at the middle point intersects AB at P.Then AP:AB is
  A.  1:4
  B.  1:4
  C.  1:4
  D.  1:4
     
   
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32. An isosceles triangle ABC is right angled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the AB and AC respectively of △ABC.If AP = a cm,AQ = b cm and ∠BAD = 15°, sin75° =
  A.  √3a/2b
  B.  √3a/2b
  C.  √3a/2b
  D.  √3a/2b
     
   
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33. ABC is an isosceles triangle such that AB = AC and AD is the median to the base BC with ∠ABC=35°.Then ∠BAD is
  A.  55°
  B.  55°
  C.  55°
  D.  55°
     
   
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34. In △ABC,BD and CE are perpendicular to AC and AB respectively.If BD=CE,then △ABC is
  A.  Isosceles
  B.  Isosceles
  C.  Isosceles
  D.  Isosceles
     
   
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35. ABC is an isosceles triangle inscribed in a circle.If AB = AC= 12√5cm and BC = 24 cm then the radius of circle is
  A.  15cm
  B.  15cm
  C.  15cm
  D.  15cm
     
   
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36. In an isosceles triangle ABC,AB =AC,XY||BC.If ∠A = 30°,then angle ∠BXY =?
  A.  105°
  B.  105°
  C.  105°
  D.  105°
     
   
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37. △ABC is isosceles having AB =AC and angleA = 40°.Bisectors PO and OQ of the exterior angles ∠ABD and ∠ACE formed by producing BC on both sides,meet at O.Then the value of ∠BOC is
  A.  70°
  B.  70°
  C.  70°
  D.  70°
     
   
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38. △ABC is an isosceles right angled triangle having ∠C = 90°.If D is any point on AB,then AD2+BD2 is equal to
  A.  2CD2
  B.  2CD2
  C.  2CD2
  D.  2CD2
     
   
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39. O And C are respectively the orthocenter and circumcenter of an acute-angle triangle PQR.The points P and O arejoined and produced to meet the side QR at S.If ∠PQS = 60° and ∠QCR = 130°,then ∠RPS =
  A.  35°
  B.  35°
  C.  35°
  D.  35°
     
   
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40. In △ABC,AD is the internal bisector of ∠A, meeting the side BC at D.If BD = 5cm,BC= 7.5 cm ,then AB:AC is
  A.  2:1
  B.  2:1
  C.  2:1
  D.  2:1
     
   
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