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Standard IX

Mathematics

Basic Constructions

Your challeng...

Question

Your challenge is to mark the points between the rays PA and PB (both included) which lie at a certain distance, say 'd', from a point P, as shown. PC = d. How many such points exist?

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Only 1 point, on the ray PA

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Only 2 points, each on the rays PA and PB

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Infinite points, between the rays PA and PB

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Solution

The correct option is D
Infinite points, between the rays PA and PB

To locate points which are equidistant from P and at a distance 'd', take a compass, with P as centre and radius as 'd', draw an arc which cuts the rays PA and PB at C and D as shown.

Now, all the points on this arc CD are at a distance 'd' from P and hence they fall into our solution domain.

Hence the number of such points are infinite.

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