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Constructions

How can we divide any line segment in a given ratio? 

Akshay Tawde

Hi Akshay Tawde !
Mark as answer and close

1. Draw any ray OP, making an acute angle with OQ.

2. Locate 5 = (m + n) points O1,O2,O3,O4 and O5 on OP so that OO1 = O1O2 = O2O3 =O3O4 = O4O5.

3. Join QO5

4. Through the point O3(m = 3), draw a line parallel to O5Q (by making an angle equal to LOO5Q) at O3 intersecting OQ at point R then, OR: RQ = 3:2.

Let us see how this method gives us the required division.

Since O3R is parallel to O5Q, therefore

       OO3/O3O5 = OR/RQ....................... (By basic proportionality theorem)

By construction, OO3/O3O5 = 3/2.

This shows that R divides OQ in the ratio 3:2

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