Suppose you are give a circle. Find out its centre by construction and justify.
The centre lies on

the line joining the mid points of any two chords

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the point of intersection of the right bisectors of any two chords of the given circle.

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on the line which bisects the angle between any two chords.

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both options A & C

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Solution

The correct option is C the point of intersection of the right bisectors of any two chords of the given circle.
$G i v e n - A c i r c l e . T o f i n d o u t - i t s c e n r e b y c o n s t r u c t i o n . C o n s t r u c t i o n - (I) A n y t h r e e p o i n t s A, B & C a r e t a k e n o n t h e c i r c u m f e r e n c e . (I I) A B & B C a r e j o i n e d . (I I I) T h e r i g h t b i s e c t o r s O M & O N o f A B & B C a r e d r a w n . O M & O N i n t e r s e c t a t O . S o O i s t h e c e n t r e o f t h e c i r c l e . J u s t i f i c a t i o n - O A, O B & O C a r e j o i n e d . O A = O B s i n c e O M i s t h e r i g h t b i s e c t o r o f A B a n d O B = O C s i n c e O N i s t h e r i g h t b i s e c t o r o f A B . ∴ O A = O B = O C . i . e A, B & C a r e e q u d i s t a n t f r o m O s i n c e t h e c e n t r e o f a c i r c l e i s e q i d i s t a n t f r o m a l l t h e p o i n t s o n t h e c i r c u m f e r e n c e . ∴ O i s t h e c e n t r e o f t h e c i r c l e . A n s - O p t i o n B .$

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Similar questions

The line segment joining any two points on the circle which passes through the centre of the circle is called a __.

The line joining the centre of a circle and the point from which two tangents are drawn bisects the angle between the tangents.

65^{\circ}

∠

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