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Question


Mention the proper order of identifying a point D on BC such that BDDC=23.
1) Join B5C and draw a line parallel to B5C from B2.
2) Identify the ratio in which the point D divides BC using the relation given.
3) Mark 5 points B1, B2, B3, B4 and B5 on BX such that they are equidistant.
4) Construct a ray BX which makes an acute angle with line segment BC.
5) The point of intersection of the parallel line from B2 with BC is the point D.


A

2, 4, 3, 1, 5

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B

1, 2, 4, 3, 5

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C

4, 3, 2, 5, 1

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D

3, 5, 2, 4, 1

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Solution

The correct option is A

2, 4, 3, 1, 5


D divides BC in the ratio 2:3. Our next obvious task, is therefore to find this point D. So, draw a raywhich makes an acute angle with side BC. Now perform the constructions required to mark D on BC such that BD:DC = 2:3.



The steps of construction:
First you need to construct the ABC. Now that you have constructed the ABC we can divide the line BC such that BD:DC = 2:3.
a) Let us start by constructing a ray BX which makes an acute angle with line segment BC.
b) Now mark B1,B2,B3,B4 and B5 on ray BX such that BB1=B1B2=B2B3=B3B4=B4B5. (This is done in order to divide BB2 and B2B5 in the ratio 2:3)
c) Now join B5C and draw B2D parallel to B5C such that the point D lies on the line segment BC. By Basic Proportionality Theorem, BDDC=BB2B2B5=23.

So, the correct order is 2, 4, 3, 1, 5.


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