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If the non-parallel sides of a trapezium...

If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

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Show that the st. Line joining the mid-points of two non-parallel sides of a trapezium is parallel to the bases and is equal to half of the sum of their lengths.

State whether True or False. Correct the statements. Distance between the two parallel sides of the trapezium is called the base of the trapezium.

E and F are the mid points of non-parallel sides AD and BC respectively of a trapezium prove that EF||AB.

If a pair of opposite sides of a cyclic quadrialteral are equal, prove that its diagonals are also equal.

The parallel sides of the trapezium are 13 cm, 25 cm and the non parallel sides are 10 cm. Find the area of the trapezium.

Two parallel sides of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.

If the length of three sides of a trapezium other than base are equal to 10 cm, then find the area of trapezium when it is maximum.

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If altitudes from two vertices of a triangle to the opposite sides are equal prove that the triangle is isosceles.

MODERN PUBLICATION-CIRCLES-EXERCISE
  1. The longest chord of a circle is a ........... of the circle.

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  2. An arc is a ........... When its ends are the ends of a diameter.

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  3. A chord is at a distance of 8 cm from the centre of a circle of radis ...

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  4. An equilateral triangle of side 9 cm.

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  5. Is every diameter of a circle also a chord?

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  6. If OA = 5 cm , AB = 8 cm and OD is perpendicular to AB, then OD is equ...

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  7. (True/ False) If AOB is a diameter of a circle and C is a point on th...

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  8. ABCd is a cyclic quadrialteral such that AB is a diameter of the circl...

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

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  10. If angleABC= 20^@m find angleAOC

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  11. angleDAB = 60^@, angleABD = 50^@ find angleACB

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  12. If arc AXB and CYD of a circle are congruent, find the ratio of AB and...

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  13. Two triangles ABC and PQR are such that the perpendiculars from A to Q...

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  14. If a diameter of a cirlce bisects each of the chords of the circle, pr...

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  15. The whole angle at the centre of a circle is :

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  16. In a triangle ABC, D is the mid point of the side AC and BD=1/2AC. Sho...

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  17. On a common hypotenuse AB, two right triangles ACB and ADB are situate...

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  18. If the non-parallel sides of a trapezium are equal, prove that it is c...

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  19. In fig, two chords AB and CD intersect each other at the point P. Prov...

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  20. Draw a circle of radius 5 cm and divide it into 6 equal sectors .

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