Latest Capgemini Aptitude Question SOLUTION: In the rectangle ABCD, the perpendicular bisector of AC divides the longer side AB in a ratio 2: 1. Then the angle between AC and BD is option A. 30 degree B. 45 degree C. 60 deg

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In the rectangle ABCD, the perpendicular bisector of AC divides the longer side AB in a ratio 2: 1. Then the angle between AC and BD is
option
A. 30 degree
B. 45 degree
C. 60 degree
D. 90 degree

Asked In Capgemini D venkatesh babu (10 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

rajiv  (10 years ago)

90.AC and BD are diagonals of rectangleangle between them is always 90

Is this solution Helpfull? Yes (25) | No (30)  

preeti negi  (10 years ago)

If PQ is the perpendicular bisector of AC, intersecting AB at E and AC at 0, then
AO = OC = AC/2
AE = 2EB = (2/3)AB

Triangles AOE and ABC are similar.
=> AO/AE = AB/AC
=> (AC/2)/{(2/3)AB} = AB/AC
=> AB = AC(rt3)/2

=> Angle CAB = 30
=> Angle between AC and BD is 60 or 120

Is this solution Helpfull? Yes (8) | No (7)  

arun  (10 years ago)

can somebody put a diagram & prove it

Is this solution Helpfull? Yes (4) | No (1)  

baibhav jena  (10 years ago)

d
angle between diagonals=90

Is this solution Helpfull? Yes (3) | No (1)  

shwetha  (9 years ago)

right answer plz

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romapanigrahi  (10 years ago)

1) Imagine that your rectangle has a longer side= 3 (which you can split as 2:1 as you have done on AB).

2) You have stated that perpendicular of Ac cuts AB as 2::1

3) It implies a right angled triangle is formed by jioning said point of cutting, two diagonals (ABCD) intersecting point and point A itself!

4) As 2 is hypotanuse of said triangle other sides are '1' and '(sq rt 3))' (along diagonal)!

5) Your first question is answerd by solving said right angle triangle as ...tan (theta)= 1/(sq rt 3) and theta=30 degrees, which is a well known relation. 30 degrees is the angle in between two sides "sq rt 3 and 2" of said right angle triangle!

Included angle between AC and BD = 30*2= 60 (by a rule of alternate angles by two parallel sides and a traversal)

Answer is 60 degrees!

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Amitabha Ghosh  (10 years ago)

Look at the bisector. Let's call the point where it crosses the line AC E and the point where it crosses the line AB F. Then triangle AEF is similar to triangle ACB. (They have the same angles, a right angle, the angle at A and the angles AFE and ACB, which must be equal.

Lets say that the line AC = 2y and AB = 3x, where AF = 2x and FB = x. Then BC = sqrt((2y)^2 - (3x)^2).

The line EF = sqrt((2x)^2 - y^2)

Now use the law of sines. BC/sin(CAB) = AC/sin(B) and EF/sin(CAB) = AF/sin(AEF).

Rearrange both of these equations in terms of sin(B) and sin(AEF). Then, because B and AEF are both right angles, you should be able to set these two equations equal to each other and solve for sin(CAB).

This should enable you to calculate the sin(CAB) and therefore the angle CAB. CAB is identical to DBA, and 180-sum equals angle AEB. .

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pooja singh  (9 years ago)

what is the right answer???

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Chirag Ranjan Lahiri  (9 years ago)

angle between diagonals=90

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Aliva Das  (9 years ago)

60 or 120 ,becuse if it is not then it cannot bisect AB in the ratio 2:1

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Ankur Agrawal  (8 years ago)

If P is the midpoint of AC and its perpendicular bisector intersects AB at Q, then triangles APQ and ABC are similar
AP/AB = AQ/AC
(1/2)(x + y)/x = (2x/3)/(x + y)
1 + y/x = 4/3
y/x = 1/3
y/x = 1/3
Angle between AC and AB = 30
Angle between AC and BD = 120 or 60

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Anushuya  (7 years ago)

AC and BD are diagonals,,so it is 90 degree

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Mansi  (7 years ago)

Let P be the mid-point of both AC and BD.
As we know angles of a rectancle are 90 deg. so since BD is a bisector, angle between BD and DC will remain 45 deg. sim. the angle between AC and CD will be 45 deg. which means DP=CP=45deg. and the three angles of a triangle are 180 deg so angle between AC and BD wiil be 180 -45-45=90 deg.
Answer=90 degree

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jeetu  (7 years ago)

30degree is the correct answer. don't check other answers in the comment.

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