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ABC is a right triagle with angle B=90^(...

ABC is a right triagle with angle `B=90^(@)` . A circle with BC as diameter meets hypotenuse AC and point D. Prove that
(i) `ACxxAD=AB^(2)`
(ii) `BD^(2)=ADxxDC`

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ICSE-TANGENTS AND INTERSECTING CHORDS-EXERCISE 18 (C)
  1. In the given figure, ABCD is a cyclicquadrilateral, PQ is tangent to t...

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  2. The given figure shows a circle with centre O and BCD is tangent to it...

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  3. ABC is a right triagle with angle B=90^(@) . A circle with BC as diame...

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  4. In the given figure AC=AE Show that (i) CP=EP (ii) BP=DP

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  5. ABCDE is a cyclic pentagon with centre of its circumcircle alt point O...

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  6. In the given figure O is the centre of the circle. Tangents at A and B...

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  7. ABC is a triangle with AB=10cm, BC=8cm and AC=6cm (not drawn to scale)...

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  8. The given figure shows a semi circle with centre O ane diameter PQ. If...

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  9. The given figure shows a circle with centre O such that chord RS is pa...

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  10. In the given figure PAT is tangent to the circle with centre O, at poi...

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  11. AB is a line segment and M is its mid point. Three semi circles are dr...

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  12. TA and TB are tangents to a circle with centre O from an external poin...

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  13. Two circles intersects in points P and Q. A secant passing through P i...

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  14. Prove that the any four vertices of a regular pentagon are concyclic (...

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  15. Chords AB and CD of a circle when extended meet at point X. Given AB =...

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  16. In the given figure find TP if AT=16 cm and AB=12 cm.

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  17. In the following figure, a circle is inscribed in th equadrilaterial A...

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  18. In the given figure, XY is the diameter of the circle and PQ is a tang...

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  19. In the given figure QAP is the tangent at point A and PBD is a straigh...

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  20. In the given figure AB is the diameter. The tangent at C meets AB prod...

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