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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.

    Ncert solutions class 10 Chapter 11-15

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

    ∴ ∠PQO = 90°

    ⇒ OQ⊥ PQ

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

    ∴ ∠PRO = 90°

    ⇒ OR ⊥ 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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