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Prove that the perpendicular at the poin...

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

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Prove that the segment joining the point of contact of two parallel tangents passes through the centre.

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If a chord is drawn through the point of contact of a tangent to a circle; then the angle which this chord makes with the given tangent are equal respectively to the angles formed in the corresponding alternate segments.

RD SHARMA-CIRCLES-All Questions
  1. If A B C is isosceles with A B=A C and C(O ,\ r) is the incircl...

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  2. In Fig. 10.54, a circle touches all the four sides of a quadrilater...

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  3. Prove that the perpendicular at the point of contact to the tangent...

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  4. Two circles touch externally at a point P . From a point T on th...

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  5. In Fig. 10.57, a circle is inscribed in a quadrilateral A B C D in ...

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  6. In Fig. 10.59, A B is a chord of length 16cm of a circle of radi...

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  7. In Fig. 10.60, P A and P B are tangents from an external point P...

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  8. In Fig. 10.61, B D C is a tangent to the given circle at point D...

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  9. In Fig. 10.62, P O|Q O . The tangents to the circle at P and Q i...

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  10. The lengths of three consecutive sides of a quadrilateral circumscr...

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  11. In Fig. 10.67, O Q : P Q=3:4 and perimeter of P O Q=60 c m . De...

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  12. In Fig. 10.72, P A and P B are tangents to the circle drawn from...

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  13. What is the distance between two parallel tangents of a circle of r...

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  14. The length of a tangent from a point A at distance 5 cm from the ce...

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  15. Two tangents T P and T Q are drawn from an external point T to a...

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  16. What is the distance between two parallel tangents to a circle of r...

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  17. In Q. No. 1, if P B=10 c m , what is the perimeter of P C D ?

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  18. In Fig. 10.74, C P and C Q are tangents to a circle with centre ...

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  19. In Fig. 10.75, A B C is circumscribing a circle. Find the lengt...

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  20. In Fig. 10.76, C P and C Q are tangents from an external point C...

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