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CBSE Class 9 Answered

prove that of all chords of circle through a given point within it, the chord which is bisected at that point is the smallest
Asked by subbusuchi1978 | 05 Nov, 2023, 10:24: AM
answered-by-expert Expert Answer
s
Figure shows a circle of radius R .  Let AB and CD are chords that is passing through a point E .
 
Chord AB is bisected at E . Chord CD is not bisected at E.
 
Perpendicular distance h1 to the chord AB  is greater than perpendicular distance h2 to the chord CD .
 
Length of chord AB  begin mathsize 14px style equals space 2 space square root of R squared space minus space h subscript 1 superscript 2 end root space end style
 
Length of chord CD  begin mathsize 14px style equals space 2 space square root of R squared space minus space h subscript 2 superscript 2 end root space end style
Since h1 > h2 ,  we get AB < CD
 
Hence , if many chords are passing through a common point within a circle ,
then length of chord that is bisected by the common point has smallest length
 
Answered by Thiyagarajan K | 05 Nov, 2023, 11:48: AM

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CBSE 9 - Maths
prove that of all chords of circle through a given point within it, the chord which is bisected at that point is the smallest
Asked by subbusuchi1978 | 05 Nov, 2023, 10:24: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
if two circles intersect at two points prove that their centres lie in the perpendicular bisector of the common chord
Asked by rameshsonkar1234ramesh | 21 Dec, 2022, 11:03: PM
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CBSE 9 - Maths
three girls Reshma Salma And Mandeep are playing a game by standing on a circle of radius 5 drawn in a park Reshma throws a ball to Salma Salma To mandip mandip to Reshma if the distance between Reshma and Salman and between Salman Mandeep 6 each what is the distance between Reshma Mandip
Asked by chalkekalyani80 | 06 Mar, 2022, 11:25: AM
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CBSE 9 - Maths
two circles of radii 5cm and 3cm intersect at two points and distance between the centres is 4cm. find the length of the common chord  
Asked by tejvinder3r | 27 Jan, 2020, 10:27: AM
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CBSE 9 - Maths
AC is the diameter of the circle whose centre is O .AB and CD are parallel chords of a circle .prove that OA = OB 
Asked by arvindhsb2005 | 14 Jan, 2020, 09:14: PM
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CBSE 9 - Maths
Q. Out of two concentric circles,the radius of the outer circle is 5 cm and the chord AC of length 8 cm is tangent to the inner circle.Find the radius of the inner circle.
Asked by sambitgenius2005 | 24 Apr, 2019, 08:03: PM
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CBSE 9 - Maths
Prove that the line joining the mid points of two parallel chords of a circle, passes through the centre of the circle.
Asked by Topperlearning User | 18 Aug, 2017, 09:07: AM
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CBSE 9 - Maths
Prove that the perpendicular from the centre of the circle to a chord bisects the chord.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 9 - Maths
AB and CD are two parallel chords of a circle such that AB = 12 cm and CD = 24 cm. The chords are on the opposite sides of the centre and the distance between them is 17 cm. Find the distance between them.
Asked by Topperlearning User | 14 Feb, 2014, 02:05: PM
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CBSE 9 - Maths
begin mathsize 12px style Two space chords space AB space and space AC space of space straight a space circle space are space equal. space Prove space that space the space centre space of space the space circle space lies space on space the space angl e space bisector space of space angle BAC. end style
Asked by Topperlearning User | 29 Apr, 2016, 02:46: PM
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