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If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

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To prove that the diagonals of a cyclic quadrilateral are equal when a pair of opposite sides are equal, we can follow these steps: ### Step-by-Step Solution 1. **Draw the Cyclic Quadrilateral**: Let \( ABCD \) be the cyclic quadrilateral, where \( A, B, C, D \) are points on the circumference of a circle. 2. **Given Information**: ...
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NCERT EXEMPLAR ENGLISH-CIRCLES-Exercise 10.3
  1. If two arcs of a circle (or of congruent circles) are congruent, then ...

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  2. If the perpendicular bisector of a chord AB of a circle PXAQBY interse...

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  3. A, B and C are three points on a circle. Prove that the perpendicular ...

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  4. Two chords A B and A C of a circle are equal. Prove that the centre of...

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  5. If a line segment joining mid-points of two chords of a circle passes ...

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  6. ABCD is such a quadrilateral that A is the centre of the circle passin...

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  7. If O is the circumcentre of a A B C and O D|B C , prove that /B O D=/...

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  8. On a common hypotenuse AB, two right angled triangles, ACB and ADB are...

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  9. Two chords AB and AC of a circle subtends angles equal to 90^(@) and 1...

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  10. If BM and CN are the perpendiculars drawn on the sides AC and BC of th...

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  11. If a line is drawn parallel to the base of an isosceles triangle to in...

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  12. If the two sides of a pair of opposite sides of a cyclic quadrilate...

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  13. The circumcentre of the DeltaABC" is O. Prove that "angleOBC+angleBAC=...

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  14. A chord of a circle is equal to the radius of the circle find the angl...

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  15. In figure, angleADC=130^(@)" and chord BC=chord BE. Find "angleCBE.

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  16. In figure, angleACB=40^(@) ." Find "angleOAB.

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  17. In Figure, A B C D is a cyclic quadrilateral whose side A B is a ...

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  18. Two circles whose centres are O and O ' intersect at Pdot Throug...

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  19. In figure, AOB is a diameter of the circle and C, D, E are any three ...

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  20. In figure, angleOAB=30^(@) and angleOCB=57^(@)." Find "angleBOC and an...

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