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The quadrilateral formed by angle bisect...

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

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Definition of Cyclic quadrilateral

The quadrilateral formed by the bisectors of the angles of a parallelogram is a

Prove that the quadrilateral formed (if possible by the internal angle bisectors of any quadrilateral is cyclic

Prove that, any rectangle is a cyclic quadrilateral.

Prove that, any rectangle is a cyclic quadrilateral.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

ABCD is a cyclic quadrilateral (see Figure). Find the angles of the cyclic quadrilateral.

The bisectors of the angles formed by producing the opposite sides of a cyclic quadrilateral (provided that they are not parallel) intersect at right angle.

TARGET PUBLICATION-CIRCLE-Additional Problems for Practice
  1. As shown in the adjoining figure , two circles centred at A and B are ...

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  2. In the adjoining figure, points A, B,C and D are on the circle . The m...

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  3. In the adjoining figure, P is the circumcentre of the DeltaABC.mangle ...

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  4. In the adjoining figure, chord LMcong chord LN, angleL=35^@ find (i)...

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  5. In the adjoining figure, A,B and C are three points on a circle with c...

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  6. In the adjoining figure, O is the centre, seg PQ is diameter , line AQ...

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  7. In the adjoining figure, m (arc XAZ)=m(arc YBW). Prove that : XY||ZW

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  8. In a cyclic quadrilateral ABCD, angleB=(5x+40)^@ and angleD=(8x+23)^@,...

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  9. square ABCD is a cyclic quadrilateral . m (arc ABC) =230^@ . Find angl...

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  10. The quadrilateral formed by angle bisectors of a cyclic quadrilateral ...

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  11. In the figure , if m ( arc DXE 0 = 100^(@) and m (arc AYC ) = 40^(@)...

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  12. In the adjoining figure, seg AB and seg AD are chords of the circle . ...

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  13. In the given figure PA=6, PB=4 and PC=8. Find PD.

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  14. In the adjoining figure. Chord MN and chord RS intersect each other at...

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  15. In the adjoining figure , chords HI and KJ intersect at point L. If KL...

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  16. In the adjoining figure, chords CB and ED intersect each other in poin...

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  17. In the adjoining figure ,seg PS is a tangent segment. Line PR is a sec...

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  18. In the given figure, a tangent segment PA touching a circle in A and a...

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  19. In the following figure , ray PA is the tangent to the circle at point...

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  20. In the adjoining figure, line AP is tangent to the circle at A, secant...

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