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The tangent at any point of a circle is ...

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

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How can you prove the converse of the above theorem. "If a line in the plane of a circle is perpendicular to the radius at its end point on the circle , then the line is tangent to the circle " .

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Choose the correct answer and give justification for each . The angles between a tangent to a circle and the radius draw at the point of contact is

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BEYOND PUBLICATION-TANGENTS AND SECANTS TO CIRCLE-EXERCISE
  1. The tangent at any point of a circle is perpendicular to the radius th...

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  2. A tangent to a circle intersects it in ………. Point (s) .

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  3. A line intersecting a circle in two points is called a ………..

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  4. Fill in the blanks. A circle can have parallel……………tangents at the mos...

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  5. The common point to a tangent and a circle is called …..

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  6. We can draw ………… tangents to a given circle .

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  7. In the given figure, O is the centre of the circle and PT is a tangent...

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  8. In the adjacent figure, Prove that BD = DC if AB = AC

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  9. The incircle of a triangle ABC touches the sides AB, BC and CA at the ...

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  10. Find the area of a quadrant of a circle whose circuemference is 88 cm.

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  11. The minute hand of a clock is 6 m long. Find the area of the face of t...

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  12. Two circles touch internally. The sum of their areas is 116 pi cm^2 an...

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  13. In the figure ABCD, find the area of the shaded region.

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  14. A chord of a circle of radius 14 cm subtends a right angle at the cent...

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  15. A circle touches all the four sides of a quadrilateral PQRS . Prove th...

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  16. Prove that the tangents at the extermities of any chord makes equal an...

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  17. Two tangents TP and TQ are drawn to a circle with centre 'O' from on e...

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  18. In two concentric circles, a chord of length 24 cm of larger circle be...

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  19. If 'O' is the centre of the circle. PA and PB are tangent segments. Sh...

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  20. If PA and PB are tangents from an external point to a circle with cen...

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  21. In the adjacent figure, BC is a tangent to the circle with centre 'O'....

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