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A tangent to a circle intersects it in …...

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

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A tangent meets a circle in……. Points .

A tangent to a circle touches it in ................ point (s).

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Draw a tangent to a given circle with center O from a point 'R' outside the circle. How many tangents can be drawn to the circle from that point? The distance of two points to the point of contact is the same.

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see figure). Find the length of TP.

Draw a circle of radius 4 cm and draw a pair of tangent to the circle, which are intersecting each other 6 cm away from the centre.

In the adjacent figure, common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.

Draw a circle of radius 5 cm . From a point 8 cm away from its centre , construct a pair of tangents to the circle . Find the lengths of tangents .

The common point of the tangent and the circle is called the point of contact and the tangents is said to touch the circle at the common point. Observe the tangents to the circle in the figures given below. How many tangents can you obtain to the circle.in all?See the points of contact. Draw radii from the points of contact. Do you see any thing special about the angle between the tangents and radii at the points of contact. All appear to be perpendicular to the corresponding tangents. How many tangents can you draw to a circle at a point?

BEYOND PUBLICATION-TANGENTS AND SECANTS TO CIRCLE-EXERCISE
  1. A tangent to a circle intersects it in ………. Point (s) .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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