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ABCD is a cyclic quadrilateral. A circle...

ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD and BC in E and F respectively. Prove that EF||DC

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ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = Ed. Prove that AD ||BC

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = Ed. Prove that EB = EC

ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.

A line parallel to BC of a triangle ABC, intersects AB and AC at D and E respectively. Prove that (AD//DB) =( AE//EC) .

ABCD is such a quadrilateral A is the centre of the circle passing through B,C and D. Prove that : angleCBD + angleCDB = 1/2 angleBAD

ABCD is a parallelogram. The circle through A,B is so drawn that it intersects AD at P and CB at Q. Prove that P,Q,C and D are concyclic.

ABCD is a quadrilateral in which AD=BC and angleADB=angleCBA . Prove that: BD=AC

A triangle A B C is inscribed in a circle with centre at O , The lines A O ,B Oa n dC O meet the opposite sides at D , E ,a n dF , respectively. Prove that 1/(A D)+1/(B E)+1/(C F)=(acosA+bcosB+ccosC)/triangle

In a quadrilateral ABCD, AO and BO are bisectors of angleA and angle B respectively. Prove that angleAOB=1/2(angleC+angleD)

In the fig. ABC, is an isosceles triangle in which AB=AC. Also D,E and F are mid point of BC, CB and AB respectively. Show that ADbotEF and AD is determined by EF

MODERN PUBLICATION-CIRCLES-EXERCISE
  1. ABCD is a cyclic quadrilateral. A circle passing through A and B meets...

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  2. The radius of a circle is 8 cm and the length of its chords is 12 cm. ...

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  3. Find the length of a chord which is at a distance of 24 cm from the ce...

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  4. A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the...

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  5. Find the length of a chord which is at a distance of 24 cm from the ce...

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  6. PQ and RS are two parallel chords of a circle whose centre is O and ra...

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  7. PQ and RS are two parallel chords of a circle whose centre is O and ra...

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  8. AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm a...

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  9. Two parallel chords of lengths 30 cm and 16 cm are drawn on the opposi...

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  10. In an equilateral triangle, prove that centroid and circumcentre coinc...

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  11. Two chords PQ and RS of a circle are parallel to each other and AB is ...

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  12. In fig., two circles with centres O, O' touch externally at a point A....

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  13. Prove that the right-bisector of a chord of a circle bisects the corre...

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  14. Two chords AB and AC of a circle are equal. Prove that the centre of t...

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  15. Two equal chords AB and CD of a circle C(O,r) when produced meet at a ...

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  16. Two equal chords AB and CD of a circle C(O,r) when produced meet at a ...

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

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  18. Prove that the perpendicular at the point of contact to the tangent to...

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  19. Diameter is the largest chord of the circle. (True/False)

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  20. PQ and RQ are chords of a circle equidistant from the centre. Prove th...

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  21. In given Fig. , AD = AE and D and E are points on BC, such that BD = ...

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