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The sum of either pair of opposite angle...

The sum of either pair of opposite angles of a cyclic quadrilateral is `180^0` OR The opposite angles of a cyclic quadrilateral are supplementary.

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Verified by Experts

TO prove`=/_A+/_C=180^@,/_B+/_DD=180^@`
Chord AB`/_ACB=/_ADB-(1)`
Chord BC`/_BAC=/_BDC-(2)`
adding equation 1 and 2
`/_ACB+/_BAC=/_ADB+/_BDC`
`/_ACB+/_BAC+/_ABC=/_ADC+/_ABC`
`/_D+/_B=180^@`
`/_B+/_D=180^@`
...
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The opposite angles of a cyclic quadrilaterals are supplimentary

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RD SHARMA-CIRCLE -All Questions
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  2. If two opposite sides of a cyclic quadrilateral are equal, then the ...

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  3. The sum of either pair of opposite angles of a cyclic quadrilateral is...

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  4. If the chord of a circle is equal to the radius of the circle, then th...

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  5. If one side of a cyclic quadrilateral is produced, then the exterior ...

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  6. If the sum of any pair of opposite angles of a quadrilateral is 180^@;...

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  7. The sum of the angles in the four segments exterior to a cyclic qua...

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  8. If the bisectors of the opposite angles /Pa n d/R of a cyclic quadrila...

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

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  10. Two diameters of a circle intersect each other at right angles. Prove ...

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  11. A B C and A D C are two right triangles with common hypotenuse A Cdot ...

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  12. In a circle with centre O , chords A Ba n dC D intersect inside the ci...

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  13. triangle ABC AND triangle ADC are two right triangles with common hypo...

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  14. Bisectors of angles A, B and C of a triangle ABC intersect its circ...

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

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  16. A Ca n dB D are chords of a circle that bisect each other. Prove that:...

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  17. Prove that the mid-point of the hypotenuse of a right triangle is eq...

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  18. In Figure, P , is any point on the chord B C of a circle such that A B...

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  19. Two chords A B and C D of a circle are parallel and a line l is the pe...

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  20. A circular park of radius 20m is situated in a colony. Three boys Anku...

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