Suppose you are given a circle. Give the construction to find its centre.

The center lies on the perpendicular bisectors of any two chords of the circle

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The center lies on the mid point of any chord of the circle

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The center lies on the bisector of the angle betwee any two chords of the circle

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Both options B & C.

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Solution

The correct option is C The center lies on the perpendicular bisectors of any two chords of the circle
$G i v e n - A c i r c l e . T o f i n d o u t - i t s c e n r e b y c o n s t r u c t i o n .$

$C o n s t r u c t i o n -$

$(I) A n y t h r e e p o i n t s A, B & C a r e t a k e n o n t h e c i r c u m f e r e n c e .$

$(I I) A B & B C a r e j o i n e d .$

$(I I I) T h e r i g h t b i s e c t o r s O M & O N o f A B & B C a r e d r a w n .$

$O M & O N i n t e r s e c t a t O .$

$S o O i s t h e c e n t r e o f t h e c i r c l e .$

$J u s t i f i c a t i o n - O A, O B & O C a r e j o i n e d .$

$O A = O B s i n c e O M i s t h e r i g h t b i s e c t o r o f A B a n d$

$O B = O C s i n c e O N i s t h e r i g h t b i s e c t o r o f A B .$

$∴ O A = O B = O C .$

$i . e A, B & C a r e e q u d i s t a n t f r o m O s i n c e t h e c e n t r e o f a c i r c l e i s e q i d i s t a n t f r o m a l l t h e p o i n t s o n t h e c i r c u m f e r e n c e .$

$∴ O i s t h e c e n t r e o f t h e c i r c l e .$

$A n s - O p t i o n A .$

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Similar questions

Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

Draw a circle of radius $4 c m .$ Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

C

3.4 c m

¯ ¯¯¯¯¯¯ ¯ A B

¯ ¯¯¯¯¯¯ ¯ A B

C

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