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`AB` is a diameter of a circle with centre `O`. A line drawn through the point `A` intersects the circle at the point `C` and the tangent through `B` at the point `D`. Prove that `(a) BD^(2)=AD.DC` . `(b) ` The area of the rectangle of formed by `AC` and `AD` for any straight line is always equal.

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CALCUTTA BOOK HOUSE-SIMILARITY-Exercise 5.2
  1. AB is a diameter of a circle with centre O. A line drawn through the p...

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  2. In DeltaPQR and DeltaDEF, (PQ)/(DE)=(QR)/(EF)=(RP)/(FD). Then which on...

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  3. In DeltaABC and DeltaDEF if /B=/E and /C=/F, then which of the followi...

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  4. In DeltaPQR and DeltaDEF,/Q=/E=42^(@), (PQ)/(DE)=(QR)/(EF) and if /F=6...

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  5. In the right-angled triangles DeltaPQR and DeltaDEF, /Q=/E= right angl...

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  6. DeltaABC and DeltaBDE are two equilateral triangles. If D is the mid-p...

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  7. If the ratio of the sides of two similar triangles be 4:9, then ratio ...

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  8. DeltaPQR~DeltaDEF and their areas are 49 sq-cm and 121 sq-cm respectiv...

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  9. Write the following sentences true or false: Any two identical image a...

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  10. C and B are two points on the straight line XY, P is an external point...

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  11. In DeltaPQR, a straight line parallel to QR intersects PQ and PR at th...

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  12. Fill the blank :All (equilateral/isosceles) triangle are always ident...

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  13. state true or false; Two equiangular triangles are always congruent.

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  14. state true or false; If the two sides of two triangles are in proport...

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  15. If the areas of two similar triangles be equal, they are .

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  16. The ratio of the areas of two similar triangels is equal to the of the...

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  17. Prove that the perimeters of two similar triangles are proportional to...

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  18. AD is a perpendiuclar drawn from the vertex A of the right-angled tria...

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  19. Fill the blank :All circles are(uniform/identical)

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  20. Fill the blank :All square are(uniform/identical)

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  21. Write the following sentences true or false: Any two identical figure ...

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