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Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals

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To prove that the circle drawn with any side of a rhombus as diameter passes through the point of intersection of its diagonals, we will follow these steps: ### Step 1: Understand the properties of a rhombus A rhombus is a quadrilateral where all sides are equal in length. The diagonals of a rhombus bisect each other at right angles (90 degrees). ### Step 2: Identify the points Let the vertices of the rhombus be \( A, B, C, D \). The diagonals \( AC \) and \( BD \) intersect at point \( M \). ...
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RD SHARMA-CIRCLE -All Questions
  1. Prove that the perpendicular bisectors of the sides of a cyclic quad...

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  2. Prove that the centre of the circle circumscribing the cyclic rectan...

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  3. Prove that the circle drawn with any side of a rhombus as diameter, ...

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  4. If the two sides of a pair of opposite sides of a cyclic quadrilater...

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  5. A B C D is a cyclic quadrilateral in which B A\ a n d\ C D when pr...

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  6. Prove that the angle in a segment greater than a semi-circle is less...

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  7. A B C D is a cyclic trapezium with A D B Cdot If /B=70^0, determine...

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  8. Prove that the line segment joining the mid-point of the hypotenuse ...

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  9. A B C D is a cyclic quadrilateral in which A C\ a n d\ B D are its d...

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  10. In Figure, two circles intersect at A\ a n d\ B . The centre of th...

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  11. In Figure, two congruent circles with centers O\ a n d\ O ' intersec...

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  12. A B C D is a cyclic quadrilateral in which /B A D=75^0,\ /A B D=58^0...

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  13. In Figure, if /A O B=80^0a n d\ /A B C=30^0, then find /C A O

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  14. If O is the circumcentre of A B C , then find the value of /O B C...

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  15. If Figure, A O C is a diameter of the circle and are A X B=1/2 arc B...

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  16. In Figure, A is the centre of the circle. A B C D is a parallelogram...

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  17. In Figure, A B is a diameter of the circle such that /A=35^0a n d\ /...

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  18. In Figure, P\ a n d\ Q are centres of two circles intersecting at B\...

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  19. In Figure, A B C D is quadrilateral inscribed in a circle with centr...

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  20. If the length of a chord of a circle is 16 cm and is at a distance o...

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