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# Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle Q.7

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Give me the best solution of class 10th of chapter constructions of exercise 11.2 of question no.7 of class 10th ncert math, how i solve this problem in easy way Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle

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1. Construction Procedure:

The required tangents can be constructed on the given circle as follows.

1. Draw a circle with the help of a bangle.

2. Draw two non-parallel chords such as AB and CD

3. Draw the perpendicular bisector of AB and CD

4. Take the centre as O where the perpendicular bisector intersects.

5. To draw the tangents, take a point P outside the circle.

6. Join the points O and P.

7. Now draw the perpendicular bisector of the line PO and midpoint is taken as M

8. Take M as centre and MO as radius draw a circle.

9. Let the circle intersects intersect the circle at the points Q and R

10. Now join PQ and PR

11. Therefore, PQ and PR are the required tangents.

Justification:

The construction can be justified by proving that PQ and PR are the tangents to the circle.

Since, O is the centre of a circle, we know that the perpendicular bisector of the chords passes through the centre.

Now, join the points OQ and OR.

We know that perpendicular bisector of a chord passes through the centre.

It is clear that the intersection point of these perpendicular bisectors is the centre of the circle.

Since, âˆ PQO is an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.

âˆ´ âˆ PQO = 90Â°

â‡’ OQâŠ¥ PQ

Since OQ is the radius of the circle, PQ has to be a tangent of the circle. Similarly,

âˆ´ âˆ PRO = 90Â°

â‡’ OR âŠ¥ PO

Since OR is the radius of the circle, PR has to be a tangent of the circle

Therefore, PQ and PR are the required tangents of a circle.

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