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Question

To construct a triangle similar to given $$\displaystyle \Delta ABC$$ with its sides $$\dfrac35$$ of that of $$\displaystyle \Delta ABC$$, a ray $$BX$$ is drawn at acute angle with $$BC$$. How many minimum no. of points should be marked on $$BX$$?


A
2
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B
3
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C
4
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D
5
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Solution

The correct option is D $$5$$
Suppose $$\triangle PQB$$ is the required triangle.
$$BQ = \dfrac35 \times BC\Rightarrow PQ = \dfrac35\times (BQ+QC) \Rightarrow 5BQ = 3BQ+3CQ\Rightarrow 2BQ = 3CQ$$, i.e, $$\dfrac{BQ}{CQ} = \dfrac32$$
Therefore, $$Q$$ divides $$BC$$ in ratio $$3:2$$. So, minimum number of points required on ray $$BX = 2+3=5$$

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Mathematics

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