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Question

Draw two intersecting lines to include an angle of 30. Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point/points exist(s)?


A

1

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B

2

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C

3

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D

4

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Solution

The correct option is D

4


Draw two lines AB and CD such that they intersect at O and AOC = 30.

We know that the locus of a point which is equidistant from two intersecting straight lines is a pair of straight lines which bisect the angles between the given lines.

So, points equidistant from these lines lie on the bisectors of AOC, AOD, DOB and BOC.

Therefore we draw the bisectors of these angles.

Now, draw a circle with O as centre and radius 2cm.

As we see from the figure above, his circle cuts OP, OR, OQ and OS at four points L, M, N and U respectively.

Hence, there are four points which are equidistant from AB and CD and 2 cm away from O.


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