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In a right Triangle ABC right angled at C.P and Q are points on sides AC and CB respectively which divide these sides in the ratio of 2:1. Prove that
`9AQ^2=9AC^2+4BC^2`

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BEYOND PUBLICATION-SIMILAR TRIANGLES-EXERCISE
  1. In a right Triangle ABC right angled at C.P and Q are points on sides ...

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  2. In triangle ABC, DE||BC and AD = 1/3 BD. If BC = 4.5cm, Find DE.

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  3. In the adjacent figure triangle AHK ~ triangle ABC. If AK = 10cm, BC ...

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  4. In the adjacent figures, S and T are points on the sides PQ and PR res...

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  5. In the adjacent figure, (OA)/(OC) = (OD)/(BC). Prove that angle A = a...

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  6. In the adjacent figure, if triangle PQS ~triangle ROQ, prove that PS||...

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  7. In the adjacent figure, QA and PB are perpendiculars to AB. IF AO= 10c...

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  8. In the adjacent figure DE||BC and (AD)/(DB) = 3/5. If AC = 4.8cm, f...

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  9. P and Q are points on sides AB and AC respectively of triangle ABC. I...

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  10. Prove that if the area of two similar triangles are equal, then they a...

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  11. In the trapezium ABCD,AB||CD and AB = 2CD. If the area of triangle AOB...

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  12. D,E,F are the mid points of the sides BC, CA and AB respectively of a ...

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  13. If two triangles are equiangular, prove that the ratio of the correspo...

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  14. If two traingles are equilatangular prove that the ratio of the corres...

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  15. In the adjacent figure, triangle ABC and triangle DBC are on the same ...

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  16. The areas of two similar triangles ABC and PQR are in the ratio 9 : 16...

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  17. In the following a, b and c denote the lenghts of the sides of a trian...

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  18. In the following a, b and c denote the lenghts of the sides of a trian...

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  19. In the following a, b and c denote the lenghts of the sides of a trian...

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  20. In the following a, b and c denote the lenghts of the sides of a trian...

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  21. Two poles of heights 23m and 30m stand on the plane ground. If the dis...

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