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Two different points P and Q are given on one side of line AB.

State whether the given below statement is True or False.

Statement: A circle can be drawn passing through the points P and Q touching the line AB at point R.

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True

False

answer is A.

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Detailed Solution

Firstly, let us plot point P in the paper.

https://www.vedantu.com/question-sets/70383021-cd97-4286-97a8-4fa4e1cbc6ef790083148806808794.png

Mark a point Q from point P such that PQ is 6cm. Now join the points P and Q.

https://www.vedantu.com/question-sets/578c24b4-4b98-441c-b8f0-e93af93b83e98571510914492670550.png

Now take a point at the center of line PQ and mark it as C such that PC = 3cm.
Here, Let us draw a circle with center C and radius 3cm. We can see that the points P and Q lie on the circle as CP and CQ are also the radii of the circle.

https://www.vedantu.com/question-sets/a522b6fe-f491-4c30-a964-b9a0e8c8f1bc8465514474665625859.png

Now let us take any point on the circle and name it as R and now draw a tangent through R.

https://www.vedantu.com/question-sets/07cf7f47-83b0-4ff3-a2f9-2b8a170fedc34425540686939718445.png

Now mark A and B points on the tangent so that we get line segment AB.

https://www.vedantu.com/question-sets/e02aa839-32c1-461f-9218-e28115817b776624309656130517674.png

Hence we get the required diagram.
So, option (1) is correct for this question.

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