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In a triangle ABC, D is the mid point of...

In a triangle ABC, D is the mid point of the side AC and `BD=1/2AC`. Show that `angleABC` is a right angle.

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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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