Answer :

The diagram is as follows:


Let PQRS be the quadrilateral which has a circle inside it with center O.


Now join AO, BO, CO, DO


From the figure, 1 = 8 [Two tangents drawn from an external point to a circle subtend equal angles at the centre.]


We can also state that 2 = 3, 4 = 5 and 6 = 7


Sum of angles in a quadrilateral is 360°


Sum of angles at the center is 360°


1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 360°


2(1 + 2 + 5 + 6) = 360°


1 + 2 + 5 + 6 = 180°


or


2(8 + 3 + 4 + 7) = 360°


8 + 3 + 4 + 7 = 180°


POQ + ROS= 180°


Also QOR + POS = 180°


[Since POQ = 1 + 2


ROS = 5 + 6


QOR = 7 + 8


POS = 3 + 4


as shown in the figure]


Hence it is proved that PQ and RS subtend supplementary angles at center.


Thus the angles subtended at the centre by a pair of opposite sides are supplementary.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Heights and Distances-IHeights and Distances-IHeights and Distances-I45 mins
Resources and Development RevisionResources and Development RevisionResources and Development Revision28 mins
Cube and CuboidCube and CuboidCube and Cuboid41 mins
History - Concept and QuestionsHistory - Concept and QuestionsHistory - Concept and Questions57 mins
Sphere and HemisphereSphere and HemisphereSphere and Hemisphere16 mins
Right Circular Cone And FrustumRight Circular Cone And FrustumRight Circular Cone And Frustum43 mins
Corrosion: Types, Pros and ConsCorrosion: Types, Pros and ConsCorrosion: Types, Pros and Cons41 mins
Right Circular CylinderRight Circular CylinderRight Circular Cylinder45 mins
Revision on Substitution and  Elimination MethodRevision on Substitution and  Elimination MethodRevision on Substitution and Elimination Method44 mins
Area Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and Concepts59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the oppositeRajasthan Board Mathematics

ABCD is a cyclic Rajasthan Board Mathematics

If the bisectors Rajasthan Board Mathematics

If in a cyclic quRajasthan Board Mathematics

One angle of a cyRajasthan Board Mathematics

In the figure, O Rajasthan Board Mathematics

In the figure, O Rajasthan Board Mathematics

In figure, some aRajasthan Board Mathematics

In figure, find aRajasthan Board Mathematics

ABCD is a paralleRajasthan Board Mathematics