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Offline Centres

Draw a circle having radius 3cm . Draw a chord XY = 5cm.

State whether the given statement is True or False:

Statement: Tangents can be drawn at point X and Y without using the centre.

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True

False

answer is A.

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Detailed Solution

Let us first draw a circle of radius 3cm by using a compass and name its centre as ‘O’.

https://www.vedantu.com/question-sets/a6482892-a226-4896-ba63-82b0d1d0e2507033559817941717521.png

Now, we will draw a chord of length 5cm and name it X and Y. Join X and Y with the centre ‘O’ of the circle.

https://www.vedantu.com/question-sets/81003c95-2c45-4844-a874-7f8c18bb25db8032545853563302893.png

Now, to draw tangents at both X and Y. We draw an angle of

90^{0}

at X and Y.
We will now draw an angle of

90^{0}

at X drawing bisectors of these two arcs give an angle of measurement

90^{0}

. Also repeat the same for Y.
These perpendicular lines are tangent lines at initial X and Y.

https://www.vedantu.com/question-sets/48d8dae7-2151-4df4-b0a3-56aea7e8d37f7057510862546355441.png

Hence, it is possible to draw tangents at point X and Y without using centre
So, option (1) is correct.
Hence, the given statement is true.

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