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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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To prove that the sum of either pair of opposite angles of a cyclic quadrilateral is \(180^\circ\), we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Cyclic Quadrilateral**: Let's denote the cyclic quadrilateral as \(ABCD\). By definition, a cyclic quadrilateral is one where all vertices lie on the circumference of a circle. 2. **Label the Angles**: ...
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Theorem 10.11 : The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

Prove that the sum of opposite pair of angles of a cyclic quadrilateral is 180^@

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

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

Complete each of the following, so as to make a true statement: A quadrilateral has ............ sides A quadrilateral has ............ angles. A quadrilateral has ............ vertices, no three of which are.... A quadrilateral has ............ diagonals. The number of pairs of adjacent angles of a quadrilateral is ...... The number of pairs of opposite angles of a quadrilateral is ...... The sum of the angles of quadrilateral is..... A diagonals of quadrilateral is a line segment that joins two ..... vertices of the quadrilateral. The sum of the angles of a quadrilateral is ......... right angles. The measure of each angle of a convex quadrilateral is ...... 180^0dot In a quadrilateral the point of intersection of the diagonals lie lies in .... of the quadrilateral. A point is in the interior of a convex quadrilateral, if it is in the ....... of its two opposite angles. A quadrilateral is convex if for each side, the remaining.... lie on the same side of the line containing the side.

The sum of the angles in the four segments exterior to a cyclic quadrilateral is equal to 6 right angles.

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

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

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

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

RD SHARMA ENGLISH-CIRCLE -All Questions
  1. If two non-parallel sides of a trapezium are equal, it is cyclic. OR A...

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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 /Aa n d/B 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 ...

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

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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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